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- Relationship between cos and cosh (03:48, 8 December 2016)
- Relationship between sinh and sin (03:49, 8 December 2016)
- Relationship between sin and sinh (05:17, 8 December 2016)
- Derivative of arcsin (23:33, 8 December 2016)
- Derivative of arcsec (23:51, 8 December 2016)
- Möbius (23:55, 8 December 2016)
- Thomae function is continuous at irrationals (00:34, 9 December 2016)
- Thomae function is discontinuous at rationals (00:34, 9 December 2016)
- Thomae function (00:36, 9 December 2016)
- Champernowne constant is transcendental (00:46, 9 December 2016)
- Stieltjes constants (00:53, 9 December 2016)
- Antiderivative of cosine integral (19:42, 10 December 2016)
- Derivative of sine integral (19:44, 10 December 2016)
- Antiderivative of sine integral (19:46, 10 December 2016)
- Chi (23:57, 10 December 2016)
- Arithmetic functions (00:04, 11 December 2016)
- Dirichlet beta (00:54, 11 December 2016)
- Book:Leonard Lewin/Structural Properties of Polylogarithms (17:42, 11 December 2016)
- Arcsinh (23:28, 11 December 2016)
- Antiderivative of arcsinh (23:29, 11 December 2016)
- Arccosh (23:42, 11 December 2016)
- Antiderivative of arccosh (23:43, 11 December 2016)
- Derivative of arctanh (23:46, 11 December 2016)
- Arctanh (23:47, 11 December 2016)
- Antiderivative of arctanh (23:48, 11 December 2016)
- Legendre chi in terms of Lerch transcendent (00:04, 12 December 2016)
- Pythagorean identity for sin and cos (18:51, 15 December 2016)
- Q-Binomial coefficient (19:44, 15 December 2016)
- Airy Ai (02:00, 18 December 2016)
- Meromorphic continuation of q-exponential E sub q (07:40, 18 December 2016)
- Q-difference equation for q-exponential E sub q (07:40, 18 December 2016)
- Q-difference equation for q-exponential E sub 1/q (07:41, 18 December 2016)
- Product representation of q-exponential E sub 1/q (07:41, 18 December 2016)
- Limit of q-exponential E sub 1/q for 0 less than q less than 1 (07:41, 18 December 2016)
- Exton q-exponential (07:55, 18 December 2016)
- Q-number of a negative (08:02, 18 December 2016)
- 1/q-number as a q-number (08:03, 18 December 2016)
- Relationship between logarithm (multivalued) and logarithm (08:32, 18 December 2016)
- Z2F1(1,1;2,-z) equals log(1+z) (08:33, 18 December 2016)
- Rising factorial (18:54, 18 December 2016)
- Q-derivative power rule (19:37, 18 December 2016)
- Q-number when a=n is a natural number (20:17, 18 December 2016)
- Second q-shifted factorial (20:27, 18 December 2016)
- Book:George E. Andrews/Special Functions (20:59, 18 December 2016)
- Q-calculus footer (21:01, 18 December 2016)
- Q-Pochhammer (21:07, 18 December 2016)
- Hurwitz zeta (01:27, 21 December 2016)
- Constant multiple rule for derivatives (01:55, 21 December 2016)
- Asymptotic behavior of Sievert integral (02:08, 21 December 2016)
- Sievert integral (02:09, 21 December 2016)
- Relationship between Sievert integral and exponential integral E (02:11, 21 December 2016)
- Relationship between tanh, inverse Gudermannian, and sin (02:31, 21 December 2016)
- Rodrigues formula for Meixner polynomial (02:39, 21 December 2016)
- Meixner polynomial (02:40, 21 December 2016)
- Relationship between Meixner polynomials and Charlier polynomials (02:40, 21 December 2016)
- Relationship between tangent, Gudermannian, and sinh (02:42, 21 December 2016)
- Paper:Tom H. Koornwinder/q-Special functions, a tutorial (02:59, 21 December 2016)
- Trigamma (03:11, 21 December 2016)
- Q-exponential e sub q (03:30, 21 December 2016)
- Q-exponential e sub 1/q (04:05, 21 December 2016)
- Arcsin (23:45, 22 December 2016)
- Spherical Hankel h (1) (23:58, 22 December 2016)
- Spherical Hankel h (2) (23:58, 22 December 2016)
- Hankel H (2) (23:58, 22 December 2016)
- Hankel H (1) (23:59, 22 December 2016)
- Elliptic function (00:00, 23 December 2016)
- Constant functions are elliptic functions (00:01, 23 December 2016)
- Derivative of the exponential function (00:10, 23 December 2016)
- Euler's formula (00:20, 23 December 2016)
- E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1 (00:31, 23 December 2016)
- E^x is greater than 1+x for nonzero real x (00:31, 23 December 2016)
- E^x is less than 1/(1-x) for nonzero real x less than 1 (00:32, 23 December 2016)
- X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 (00:33, 23 December 2016)
- X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 (00:34, 23 December 2016)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 (00:34, 23 December 2016)
- E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0 (00:35, 23 December 2016)
- E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936 (00:37, 23 December 2016)
- Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1 (00:37, 23 December 2016)
- Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z)) (00:39, 23 December 2016)
- Floor (00:41, 23 December 2016)
- Planck radiation (00:47, 23 December 2016)
- Ramanujan tau inequality (00:51, 23 December 2016)
- Ramanujan tau is multiplicative (00:53, 23 December 2016)
- Ramanujan tau of a power of a prime (00:53, 23 December 2016)
- Ramanujan tau (00:53, 23 December 2016)
- Incomplete beta function (01:56, 23 December 2016)
- Identity (23:02, 25 December 2016)
- Kelvin functions footer (23:21, 25 December 2016)
- Q-derivative (04:05, 26 December 2016)
- Q-number (04:17, 26 December 2016)
- Q-factorial (04:23, 26 December 2016)
- Q-exponential E sub q (04:27, 26 December 2016)
- Q-exponential E sub 1/q (04:30, 26 December 2016)
- Derivative of arccosh (07:00, 1 January 2017)
- *-c functions footer (01:37, 5 January 2017)
- Depreciated trigonometric functions footer (02:30, 5 January 2017)
- Derivative of versine (02:33, 5 January 2017)
- Versine (02:33, 5 January 2017)
- Antiderivative of versine (02:34, 5 January 2017)
- Derivative of sine (02:46, 5 January 2017)
- Derivative of cosecant (02:48, 5 January 2017)
- Harmonic number (03:12, 5 January 2017)
- Relationship between Bessel J and hypergeometric 0F1 (06:00, 10 January 2017)
- Hypergeometric 0F0 (06:04, 10 January 2017)
- Hypergeometric 1F0 (06:04, 10 January 2017)
- Hypergeometric 1F2 (06:06, 10 January 2017)
- Paper:Thomas Clausen/Uber die function sin(φ)+sin(2φ)/2^2+sin(3φ)/3^2+etc. (06:38, 10 January 2017)
- Böhmer C (06:51, 10 January 2017)
- Böhmer S (06:51, 10 January 2017)
- Cahen's constant (07:17, 10 January 2017)
- Sylvester's sequence (07:21, 10 January 2017)
- Dirichlet function (07:29, 10 January 2017)
- Dirichlet function is nowhere continuous (07:31, 10 January 2017)
- Bessel J in terms of Bessel-Clifford (10:44, 11 January 2017)
- Relationship between Bessel-Clifford and hypergeometric 0F1 (10:46, 11 January 2017)
- Derivative of Bessel-Clifford (10:48, 11 January 2017)
- Reciprocal gamma (10:50, 11 January 2017)
- Reciprocal gamma is entire (10:50, 11 January 2017)
- Number theory functions footer (11:15, 11 January 2017)
- Book:Johann Heinrich Graf/Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale (05:14, 21 January 2017)
- Book:Leonard Lewin/Polylogarithms and Associated Functions/Second Edition (05:15, 21 January 2017)
- Book:Michael Wilensky/Ueber Besselsche Funktionen (05:15, 21 January 2017)
- Book:Victor Kac/Quantum Calculus (05:16, 21 January 2017)
- Paper:D.S. McAnally/q-exponential and q-gamma functions. I. q-exponential functions (05:22, 21 January 2017)
- Book:Bernard Dwork/Generalized hypergeometric functions (02:23, 15 February 2017)
- Book:W.N. Bailey/Generalized Hypergeometric Series (02:34, 15 February 2017)
- Secant (20:45, 26 February 2017)
- Pi is irrational (22:22, 11 March 2017)
- Integral representation of polygamma for Re(z) greater than 0 (22:45, 17 March 2017)
- Value of polygamma at 1 (22:45, 17 March 2017)
- Value of polygamma at positive integer (22:45, 17 March 2017)
- Value of polygamma at 1/2 (22:45, 17 March 2017)
- Value of derivative of trigamma at positive integer plus 1/2 (22:45, 17 March 2017)
- Polygamma recurrence relation (22:46, 17 March 2017)
- Polygamma reflection formula (22:46, 17 March 2017)
- Polygamma (22:47, 17 March 2017)
- Polygamma multiplication formula (22:51, 17 March 2017)
- Series for polygamma in terms of Riemann zeta (22:55, 17 March 2017)
- General Dirichlet series (23:16, 17 March 2017)
- Book:G.H. Hardy/The General Theory Of Dirichlet's Series (23:27, 17 March 2017)
- Dirichlet series (23:27, 17 March 2017)
- Prime zeta P (23:29, 17 March 2017)
- Riemann zeta as integral of monomial divided by an exponential (23:38, 17 March 2017)
- Riemann zeta as contour integral (23:42, 17 March 2017)
- Riemann zeta at even integers (23:57, 17 March 2017)
- Functional equation for Riemann zeta (00:00, 18 March 2017)
- Functional equation for Riemann zeta with cosine (15:18, 18 March 2017)
- Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann (15:23, 18 March 2017)
- Functional equation for Riemann xi (15:27, 18 March 2017)
- Riemann-Landau xi (15:28, 18 March 2017)
- Riemann-Landau xi is even (15:29, 18 March 2017)
- Riemann xi (15:31, 18 March 2017)
- Pell constant (20:15, 25 March 2017)
- Error function is odd (03:41, 28 March 2017)
- Haversine (03:45, 28 March 2017)
- Covercosine (03:47, 28 March 2017)
- Hacovercosine (03:50, 28 March 2017)
- Havercosine (03:51, 28 March 2017)
- Vercosine (03:51, 28 March 2017)
- Hacoversine (03:52, 28 March 2017)
- Exsecant (04:11, 28 March 2017)
- Integration by parts (21:11, 28 March 2017)
- Antiderivative of arccos (21:15, 28 March 2017)
- Antiderivative of arcsin (22:45, 28 March 2017)
- Erdős-Borwein Constant is irrational (23:49, 25 April 2017)
- Derivative of secant (00:34, 26 April 2017)
- Derivative of tangent (00:35, 26 April 2017)
- Bessel-Clifford (16:03, 29 April 2017)
- Bessel functions footer (16:21, 29 April 2017)
- Komornik–Loreti constant (23:05, 8 May 2017)
- Riemann zeta (18:40, 12 May 2017)
- Golden ratio (00:21, 24 May 2017)
- Fibonacci zeta function (00:25, 24 May 2017)
- Paper:Edmund Landau/Sur la série des inverse de nombres de Fibonacci (00:27, 24 May 2017)
- Paper:Maruti Ram Murty/The Fibonacci Zeta Function (00:28, 24 May 2017)
- Sum of odd indexed Fibonacci numbers (00:29, 24 May 2017)
- Sum of even indexed Fibonacci numbers (00:30, 24 May 2017)
- Sum of Fibonacci numbers (00:15, 25 May 2017)
- Sum of Lucas numbers (00:19, 25 May 2017)
- F(n+1)F(n-1)-F(n)^2=(-1)^n (00:21, 25 May 2017)
- L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) (00:25, 25 May 2017)
- L(n)=F(n+1)+F(n-1) (00:28, 25 May 2017)
- F(2n+1)=F(n+1)^2+F(n)^2 (00:29, 25 May 2017)
- F(2n)=F(n+1)^2-F(n-1)^2 (00:30, 25 May 2017)
- F(2n)=F(n)L(n) (00:32, 25 May 2017)
- F(n+m+1)=F(n+1)F(m+1)+F(n)F(m) (00:33, 25 May 2017)
- Sum of squares of Fibonacci numbers (00:35, 25 May 2017)
- L(n)^2-5F(n)^2=4(-1)^n (00:37, 25 May 2017)
- L(-n)=(-1)^nL(n) (00:39, 25 May 2017)
- Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I (00:41, 25 May 2017)
- Catalan's identity (00:52, 25 May 2017)
- Lucas numbers (00:57, 25 May 2017)
- Binet's formula (22:32, 25 May 2017)
- F(-n)=(-1)^(n+1)F(n) (22:33, 25 May 2017)
- Paper:John H. Halton/On a General Fibonacci Identity (22:33, 25 May 2017)
- Paper:Richard Askey/The q-Gamma and q-Beta functions (00:12, 30 May 2017)
- Q-Gamma (00:13, 30 May 2017)
- Q-Gamma at z+1 (00:17, 30 May 2017)
- Paper:Daniel S. Moak/The q-gamma function for q greater than 1 (00:18, 30 May 2017)
- N^2=T(n)+T(n-1) (01:27, 30 May 2017)
- T(n+1)=T(n)+n+1 (01:28, 30 May 2017)
- T(n)=n(n+1)/2 (01:28, 30 May 2017)
- T(n)^2=T(T(n))+T(T(n)-1) (01:30, 30 May 2017)
- T(n+1)^2-T(n)^2=(n+1)^3 (01:31, 30 May 2017)
- Triangular numbers (01:32, 30 May 2017)
- Paper:V.E. Hoggatt, Jr/Triangular numbers (01:33, 30 May 2017)
- Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I (02:02, 30 May 2017)
- Limit of quotient of consecutive Fibonacci numbers (23:53, 6 June 2017)
- Book:Ioannis Dimitrios Avgoustis/Definite Integration using the Generalized Hypergeometric Functions (02:36, 8 June 2017)
- Coshc (19:08, 12 June 2017)
- Hypergeometric 3F2 (20:21, 17 June 2017)
- Hypergeometric 0F1 (20:22, 17 June 2017)
- Hypergeometric 0F3 (20:24, 17 June 2017)
- Hypergeometric 2F0 (20:27, 17 June 2017)
- Hypergeometric 4F1 (20:27, 17 June 2017)
- Hypergeometric 1F1 (20:31, 17 June 2017)
- Hypergeometric 2F3 (20:31, 17 June 2017)
- Jackson q-Bessel (2) (21:38, 17 June 2017)
- Jackson q-Bessel (1) (21:38, 17 June 2017)
- Basic hypergeometric series psi (21:38, 17 June 2017)
- Exponential e in terms of basic hypergeometric phi (21:39, 17 June 2017)
- Hypergeometric functions footer (22:37, 18 June 2017)
- Reciprocal Riemann zeta in terms of Mobius (19:31, 21 June 2017)
- Book:Andrew Gray/A Treatise on Bessel Functions (19:38, 21 June 2017)
- Sine integral (00:42, 25 June 2017)
- Error function (00:43, 25 June 2017)
- Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry (03:07, 25 June 2017)
- Square numbers (03:26, 25 June 2017)
- Reciprocal Fibonacci constant (03:40, 25 June 2017)
- Legendre chi (17:48, 25 June 2017)
- Weierstrass function is continuous (17:51, 25 June 2017)
- Weierstrass function is nowhere differentiable (17:52, 25 June 2017)
- Weierstrass nowhere differentiable function (17:54, 25 June 2017)
- Darboux function (18:02, 25 June 2017)
- Schwarz function (18:03, 25 June 2017)
- Book:Johan Thim/Continuous Nowhere Differentiable Functions (18:04, 25 June 2017)
- E is limit of (1+1/n)^n (19:20, 25 June 2017)
- Log base a in terms of logarithm base b (19:23, 25 June 2017)
- Log e(z)=log(z) (19:26, 25 June 2017)
- Log 10(z)=log(z)/log(10) (19:27, 25 June 2017)
- Log 10(z)=log 10(e)log(z) (19:29, 25 June 2017)
- Log(z)=log(10)log 10(z) (19:30, 25 June 2017)
- Logarithm (multivalued) (19:33, 25 June 2017)
- E (19:35, 25 June 2017)
- Logarithm base a (19:36, 25 June 2017)
- Limit of log(x)/x^a=0 (19:43, 25 June 2017)
- Limit of x^a log(x)=0 (19:46, 25 June 2017)
- X/(1+x) less than log(1+x) (19:49, 25 June 2017)
- Log(1+x) less than x (19:50, 25 June 2017)
- X less than -log(1-x) (19:51, 25 June 2017)
- -log(1-x) less than x/(1-x) (19:53, 25 June 2017)
- Abs(log(1-x)) less than 3x/2 (19:54, 25 June 2017)
- Log(x) less than or equal to x-1 (19:56, 25 June 2017)
- Log(x) less than or equal to n(x^(1/n)-1) (19:57, 25 June 2017)
- Abs(log(1+z)) less than or equal to -log(1-abs(z)) (19:59, 25 June 2017)
- Log(1+z) as continued fraction (20:04, 25 June 2017)
- Jacobi theta footer (20:23, 25 June 2017)
- Jacobi theta 1 (20:23, 25 June 2017)
- Jacobi theta 2 (20:23, 25 June 2017)
- Jacobi theta 3 (20:23, 25 June 2017)
- Jacobi theta 4 (20:24, 25 June 2017)
- Logarithm and friends footer (20:25, 25 June 2017)
- Polylogarithm (20:28, 25 June 2017)
- Petr function (20:34, 25 June 2017)
- The Petr function is nowhere differentiable (20:34, 25 June 2017)
- The Petr function is continuous (20:35, 25 June 2017)
- Mersenne numbers (15:12, 27 June 2017)
- Beta in terms of power of t over power of (1+t) (01:16, 1 July 2017)
- Derivative of cosine (01:27, 1 July 2017)
- Derivative of cotangent (01:29, 1 July 2017)
- Derivative of Legendre chi 2 (01:31, 1 July 2017)
- Differential equation for Jacobi P (01:33, 1 July 2017)
- Integral of log of inverse erf from 0 to 1 (01:54, 1 July 2017)
- Log a(b)=1/log b(a) (02:07, 1 July 2017)
- Logarithmic derivative of Riemann zeta in terms of series over primes (02:17, 1 July 2017)
- Relationship between the Fransén–Robinson constant, e, pi, and logarithm (03:06, 1 July 2017)
- Series for log(riemann zeta) over primes (03:09, 1 July 2017)
- Taylor series of cosine (03:18, 1 July 2017)
- Taylor series of sine (03:19, 1 July 2017)
- Upper incomplete gamma (03:22, 1 July 2017)
- Champernowne constant (17:10, 1 July 2017)
- Sine (17:34, 1 July 2017)
- Derivative of cosine integral (04:47, 7 July 2017)
- Silver ratio (04:49, 7 July 2017)
- Cosecant (15:39, 10 July 2017)
- Bessel Y (15:39, 10 July 2017)
- Devil's staircase is continuous (15:49, 10 July 2017)
- Devil's staircase is not absolutely continuous (15:50, 10 July 2017)
- Debye function (15:56, 10 July 2017)
- Ramanujan theta function (16:02, 10 July 2017)
- Devil's staircase (16:03, 10 July 2017)
- Cosine integral (15:43, 11 July 2017)
- Unit step function (22:08, 26 August 2017)
- Two-dimensional Laplace transform (22:08, 26 August 2017)
- Airy Bi (16:07, 21 October 2017)
- Period of tanh (22:23, 21 October 2017)
- Pythagorean identity for sinh and cosh (22:25, 21 October 2017)
- Pythagorean identity for tanh and sech (22:26, 21 October 2017)
- Pythagorean identity for coth and csch (22:29, 21 October 2017)
- Sum of cosh and sinh (22:30, 21 October 2017)
- Difference of cosh and sinh (22:33, 21 October 2017)
- Sinh is odd (22:34, 21 October 2017)
- Cosh is even (22:35, 21 October 2017)
- Tanh is odd (22:36, 21 October 2017)
- Sinh of a sum (22:37, 21 October 2017)
- Cosh of a sum (22:39, 21 October 2017)
- Tanh of a sum (22:40, 21 October 2017)
- Halving identity for sinh (22:43, 21 October 2017)
- Halving identity for cosh (22:46, 21 October 2017)
- Halving identity for tangent (1) (22:48, 21 October 2017)
- Halving identity for tangent (2) (22:49, 21 October 2017)
- Halving identity for tangent (3) (22:51, 21 October 2017)
- Doubling identity for sinh (1) (22:52, 21 October 2017)
- Doubling identity for sinh (2) (22:53, 21 October 2017)
- Doubling identity for cosh (1) (22:54, 21 October 2017)
- Doubling identity for cosh (2) (23:15, 21 October 2017)
- Doubling identity for cosh (3) (23:16, 21 October 2017)
- Sech (23:35, 21 October 2017)
- Csch (23:35, 21 October 2017)
- Exponential (23:37, 21 October 2017)
- Tanh (23:43, 21 October 2017)
- Cosh (23:44, 21 October 2017)
- Sinh (23:44, 21 October 2017)
- Dawson D- (00:12, 29 October 2017)
- Dawson D+ (00:21, 29 October 2017)
- Integral representation of Struve function (16:11, 4 November 2017)
- Integral representation of Struve function (2) (16:14, 4 November 2017)
- Recurrence relation for Struve fuction (16:26, 4 November 2017)
- Recurrence relation for Struve function (2) (16:27, 4 November 2017)
- Integral representation of Struve function (3) (19:53, 4 November 2017)
- Dirichlet eta (20:58, 5 November 2017)
- Bernstein B (01:54, 26 November 2017)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (22:07, 19 December 2017)
- Cosine (22:09, 19 December 2017)
- T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (22:14, 19 December 2017)
- Relationship between Chebyshev T and hypergeometric 2F1 (22:32, 19 December 2017)
- Relationship between Chebyshev T and Gegenbauer C (22:33, 19 December 2017)
- Orthogonality of Chebyshev T on (-1,1) (22:36, 19 December 2017)
- Relationship between Chebyshev U and hypergeometric 2F1 (22:43, 19 December 2017)
- Relationship between Chebyshev U and Gegenbauer C (22:49, 19 December 2017)
- Orthogonality of Chebyshev U on (-1,1) (22:50, 19 December 2017)
- Orthogonality relation for cosine on (0,pi) (22:52, 19 December 2017)
- Book:T.S. Chihara/An Introduction to Orthogonal Polynomials (22:52, 19 December 2017)
- Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (22:54, 19 December 2017)
- Orthogonality of Gegenbauer C on (-1,1) (23:45, 19 December 2017)
- (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x) (23:47, 19 December 2017)
- NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (23:48, 19 December 2017)
- (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (01:26, 20 December 2017)
- NC n^(lambda)(x)=(n-1+2lambda)xC (n-1)^(lambda)(x)-2lambda(1-x^2)C (n-2)^(lambda-1)(x) (01:28, 20 December 2017)
- Gegenbauer C (01:29, 20 December 2017)
- C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x) (01:29, 20 December 2017)
- Signed Lah numbers (01:46, 20 December 2017)
- Unsigned Lah numbers (01:46, 20 December 2017)
- D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (00:50, 21 December 2017)
- Derivative of Struve H0 (00:51, 21 December 2017)
- D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) (00:55, 21 December 2017)
- H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (00:57, 21 December 2017)
- H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (01:03, 21 December 2017)
- H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) (01:05, 21 December 2017)
- H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (01:05, 21 December 2017)
- Struve function (01:09, 21 December 2017)
- Euler totient (01:58, 21 December 2017)
- Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (02:41, 21 December 2017)
- Laplace transform (03:37, 21 December 2017)
- Elliptic K (04:48, 21 December 2017)
- K(m)=(pi/2)2F1(1/2,1/2;1;m) (04:50, 21 December 2017)
- E(m)=(pi/2)2F1(-1/2,1/2;1;m) (04:52, 21 December 2017)
- Elliptic E (04:54, 21 December 2017)
- Log((1+z)/(1-z)) as continued fraction (04:56, 21 December 2017)
- Derivative of the logarithm (04:59, 21 December 2017)
- Nth derivative of logarithm (05:01, 21 December 2017)
- Logarithm (05:03, 21 December 2017)
- Antiderivative of the logarithm (05:05, 21 December 2017)
- Book:Milton Abramowitz/Handbook of mathematical functions (05:08, 21 December 2017)
- Fresnel C (05:10, 21 December 2017)
- Book:Earl David Rainville/Special Functions (05:19, 21 December 2017)
- Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k)) (05:25, 21 December 2017)
- Primorial (14:36, 23 December 2017)
- Paper:Harvey Dubner/Factorial and Primorial Primes (14:42, 23 December 2017)
- E (0,1)(z)=1/(1-z) for abs(z) less than 1 (21:27, 2 January 2018)
- E(2,1)(z)=cosh(sqrt(z)) (21:33, 2 January 2018)
- E(1,1)(z)=exp(z) (21:34, 2 January 2018)
- Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications (21:35, 2 January 2018)
- Mittag-Leffler (21:35, 2 January 2018)
- E(2,1)(-z^2)=cos(z) (21:55, 2 January 2018)
- Signum (05:12, 11 February 2018)
- Q-Hurwitz zeta (04:51, 12 February 2018)
- Q-zeta (04:51, 12 February 2018)
- Paper:Yilmaz Simsek/q-Dedekind type sums related to q-zeta function and basic L-series (04:52, 12 February 2018)
- Dedekind eta (05:20, 12 February 2018)
- Integral of Bessel J for nu=1 (23:18, 20 February 2018)
- Coth of a sum (01:48, 24 February 2018)
- Integral of (z^n)log(z)dz=(z^(n+1)/(n+1))log(z)-z^(n+1)/(n+1)^2 for integer n neq -1 (02:01, 24 February 2018)
- Catalan's constant (15:40, 25 February 2018)
- Catalan's constant using Legendre chi (15:46, 25 February 2018)
- Matrix e^A=limit of (I+A/s)^s (03:10, 26 February 2018)
- Matrix exponential (03:10, 26 February 2018)
- Modular form (03:20, 26 February 2018)
- Book:Nicholas Higham/Functions of Matrices: Theory and Computation (03:22, 26 February 2018)
- Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 (20:56, 3 March 2018)
- Gamma function written as a limit of a factorial, exponential, and a rising factorial (20:56, 3 March 2018)
- Gamma function written as infinite product (20:56, 3 March 2018)
- Reciprocal gamma written as an infinite product (20:56, 3 March 2018)
- Euler-Mascheroni constant (20:57, 3 March 2018)
- Beta as improper integral (20:57, 3 March 2018)
- B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (20:57, 3 March 2018)
- Beta is symmetric (20:57, 3 March 2018)
- Beta as product of gamma functions (20:58, 3 March 2018)
- B(x,y+1)=(y/x)B(x+1,y) (20:58, 3 March 2018)
- B(x,y+1)=(y/(x+y))B(x,y) (20:58, 3 March 2018)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (20:58, 3 March 2018)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (20:58, 3 March 2018)
- B(x,y)B(x+y,z)B(x+y+z,u)=Gamma(x)Gamma(y)Gamma(z)Gamma(u)/Gamma(x+y+z+u) (21:01, 3 March 2018)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (21:01, 3 March 2018)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (21:02, 3 March 2018)
- B(x,y)=2^(1-x-y)integral (1+t)^(x-1)(1-t)^(y-1)+(1+t)^(y-1)(1-t)^(x-1) dt (21:02, 3 March 2018)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (21:02, 3 March 2018)
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (21:03, 3 March 2018)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (21:03, 3 March 2018)
- Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y) (21:03, 3 March 2018)
- Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y) (21:03, 3 March 2018)
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (21:03, 3 March 2018)
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (21:03, 3 March 2018)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (21:04, 3 March 2018)
- Beta in terms of sine and cosine (21:04, 3 March 2018)
- Digamma (23:21, 3 March 2018)
- Digamma at 1 (23:22, 3 March 2018)
- Digamma functional equation (23:22, 3 March 2018)
- Digamma at n+1 (23:22, 3 March 2018)
- Digamma at z+n (23:22, 3 March 2018)
- Lerch transcendent (23:22, 3 March 2018)
- Dilogarithm (23:22, 3 March 2018)
- Relationship between dilogarithm and log(1-z)/z (23:23, 3 March 2018)
- Li2(z)=zPhi(z,2,1) (23:23, 3 March 2018)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (23:23, 3 March 2018)
- Bernoulli numbers (23:23, 3 March 2018)
- Hypergeometric 2F1 (23:23, 3 March 2018)
- (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0 (23:23, 3 March 2018)
- (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0 (23:23, 3 March 2018)
- (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 (23:24, 3 March 2018)
- C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 (23:24, 3 March 2018)
- (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0 (23:24, 3 March 2018)
- (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0 (23:24, 3 March 2018)
- Pochhammer (23:25, 3 March 2018)
- Pochhammer symbol with non-negative integer subscript (23:25, 3 March 2018)
- 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) (23:25, 3 March 2018)
- 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) (23:25, 3 March 2018)
- 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (23:25, 3 March 2018)
- 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2) (23:25, 3 March 2018)
- 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) (23:25, 3 March 2018)
- 1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4) (23:26, 3 March 2018)
- Basic hypergeometric phi (23:26, 3 March 2018)
- 1Phi0(a;;z) as infinite product (23:26, 3 March 2018)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (23:26, 3 March 2018)
- (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) (23:26, 3 March 2018)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (23:27, 3 March 2018)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (23:27, 3 March 2018)
- Euler numbers (01:04, 4 March 2018)
- Euler E (01:05, 4 March 2018)
- Euler E generating function (01:05, 4 March 2018)
- Euler E n'(x)=nE n-1(x) (01:07, 4 March 2018)
- Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition (05:39, 4 March 2018)
- Bessel J (05:41, 4 March 2018)
- Kelvin ber (05:41, 4 March 2018)
- Kelvin ker (05:42, 4 March 2018)
- Kelvin bei (05:42, 4 March 2018)
- Kelvin kei (05:42, 4 March 2018)
- Book:Arthur Erdélyi/Higher Transcendental Functions Volume III (05:44, 4 March 2018)
- Book:Arthur Erdélyi/Higher Transcendental Functions Volume II (05:44, 4 March 2018)
- Coth (05:53, 4 March 2018)
- Z coth(z) = 2z/(e^(2z)-1) + z (05:57, 4 March 2018)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (06:03, 4 March 2018)
- Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (06:05, 4 March 2018)
- Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (06:07, 4 March 2018)
- Cauchy pdf (15:39, 9 March 2018)
- Cauchy cdf (15:41, 9 March 2018)
- Arcsin pdf (15:44, 9 March 2018)
- Exponential pdf (03:10, 12 March 2018)
- Exponential cdf (03:11, 12 March 2018)
- Laplace cdf (03:16, 12 March 2018)
- Laplace pdf (03:18, 12 March 2018)
- Normal pdf (03:22, 12 March 2018)
- Normal cdf (03:26, 12 March 2018)
- Continuous uniform pdf (03:31, 12 March 2018)
- Continuous uniform cdf (03:33, 12 March 2018)
- Arcsin cdf (03:35, 12 March 2018)
- Associated Laguerre L (13:38, 15 March 2018)
- Generating function for Laguerre L (14:08, 15 March 2018)
- L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) (14:15, 15 March 2018)
- L n(0)=1 (14:17, 15 March 2018)
- L n'(0)=-n (14:18, 15 March 2018)
- Kronecker delta (14:21, 15 March 2018)
- Orthogonality of Laguerre L (14:30, 15 March 2018)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (14:32, 15 March 2018)
- XL n'(x)=nL n(x)-n L (n-1)(x) (14:35, 15 March 2018)
- L n'(x)=-Sum L k(x) (14:36, 15 March 2018)
- Laguerre L (14:37, 15 March 2018)
- Hypergeometric pFq (14:42, 15 March 2018)
- T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n (19:18, 15 March 2018)
- U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (19:22, 15 March 2018)