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- Integral representation of Struve function (3) (3 revisions)
- 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z (3 revisions)
- Logarithmic derivative of Riemann zeta in terms of series over primes (3 revisions)
- Relationship between cot and coth (3 revisions)
- Absolute convergence of secant zeta function (3 revisions)
- Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm (3 revisions)
- Series for log(z+a) for positive a and Re(z) greater than -a (3 revisions)
- Chaitin's constant (3 revisions)
- Derivative of Struve H0 (3 revisions)
- Logarithm of exponential (3 revisions)
- Mersenne numbers (3 revisions)
- Relationship between arcsin and arccsc (3 revisions)
- Riemann zeta as contour integral (3 revisions)
- Böhmer C (3 revisions)
- 2F1(1/2,1;3/2;-z^2)=arctan(z)/z (3 revisions)
- Log a(b)=1/log b(a) (3 revisions)
- X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 (3 revisions)
- Relationship between coth, inverse Gudermannian, and csc (3 revisions)
- Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt (3 revisions)
- Beta in terms of power of t over power of (1+t) (3 revisions)
- Book:T.S. Chihara/An Introduction to Orthogonal Polynomials (3 revisions)
- Pi is irrational (3 revisions)
- Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 (3 revisions)
- Derivative of arccos (3 revisions)
- Logarithm of product is a sum of logarithms (3 revisions)
- Relationship between sine, Gudermannian, and tanh (3 revisions)
- Integral representation of polygamma 2 (3 revisions)
- Faddeeva function (3 revisions)
- E^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0) (3 revisions)
- Relationship between tangent, Gudermannian, and sinh (3 revisions)
- Sum of values of sinc (3 revisions)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (3 revisions)
- Hypergeometric 1F2 (3 revisions)
- Paper:Harvey Dubner/Factorial and Primorial Primes (3 revisions)
- Riemann-Siegel Z (3 revisions)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (3 revisions)
- Q-Euler formula for E sub q (3 revisions)
- Derivative of arccosh (3 revisions)
- Bessel J in terms of Bessel-Clifford (3 revisions)
- Relationship between cos and cosh (3 revisions)
- Relationship between Chebyshev T and Gegenbauer C (3 revisions)
- Modular form (3 revisions)
- Relationship between coth and csch (3 revisions)
- Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition (3 revisions)
- Book:F.E. Relton/Applied Bessel Functions (3 revisions)
- Paper:James Whitbread Lee Glaisher/On certain definite integrals involving the exponential-integral (3 revisions)
- Integral of inverse erf from 0 to 1 (3 revisions)
- Exponential e in terms of basic hypergeometric phi (3 revisions)
- L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) (3 revisions)
- Q-Euler formula for e sub q (3 revisions)
- Derivative of arccot (3 revisions)
- Logarithm of quotient of Jacobi theta 2 equals the log of a quotient of cosines + a sum of sines (3 revisions)
- Mills' constant (3 revisions)
- Doubly periodic function (3 revisions)
- Book:Johan Thim/Continuous Nowhere Differentiable Functions (3 revisions)
- Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I (3 revisions)
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (3 revisions)
- Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3 (3 revisions)
- Fermat numbers (3 revisions)
- Dawson D- (3 revisions)
- Reciprocal Riemann zeta (3 revisions)
- Lower incomplete gamma (3 revisions)
- Relationship between Chebyshev T and hypergeometric 2F1 (3 revisions)
- Halving identity for tangent (1) (3 revisions)
- Legendre chi in terms of polylogarithm (3 revisions)
- Q-difference equation for q-exponential E sub 1/q (3 revisions)
- Q-number when a=n is a natural number (3 revisions)
- Weierstrass elementary factors inequality (3 revisions)
- Havercosine (3 revisions)
- Integral of log of inverse erf from 0 to 1 (3 revisions)
- Antiderivative of inverse error function (3 revisions)
- Derivative of arccoth (3 revisions)
- Asymptotic behavior of Sievert integral (3 revisions)
- Minkowski question mark (3 revisions)
- Reciprocal Riemann zeta in terms of Mobius (3 revisions)
- Lucas (3 revisions)
- Digamma at z+n (3 revisions)
- Relationship between the Fransén–Robinson constant, e, pi, and logarithm (3 revisions)
- Q-difference equation for q-exponential E sub q (3 revisions)
- Relationship between Struve function and hypergeometric pFq (3 revisions)
- Haversine (3 revisions)
- 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) (3 revisions)
- Q-Fibonacci polynomials (3 revisions)
- Gamma function written as a limit of a factorial, exponential, and a rising factorial (3 revisions)
- Dickson polynomial (3 revisions)
- Weierstrass sigma (3 revisions)
- E(1,1)(z)=exp(z) (3 revisions)
- Paper:Tom H. Koornwinder/q-Special functions, a tutorial (3 revisions)
- Rodrigues formula for Meixner polynomial (3 revisions)
- Integration by parts (3 revisions)
- Sum of odd indexed Fibonacci numbers (3 revisions)
- Tetrahedral numbers (3 revisions)
- Value of polygamma at positive integer (3 revisions)
- Relationship between the Gegenbauer C polynomials and the Jacobi P polynomials (3 revisions)
- 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) (3 revisions)
- Book:Richard Beals/Special functions, a graduate text (3 revisions)
- Series for log(Riemann zeta) in terms of Mangoldt function (3 revisions)
- Cell (3 revisions)
- Derivative of Jacobi theta 1 at 0 (3 revisions)
- Nielsen-Ramanujan sequence (3 revisions)
- Paper:John H. Halton/On a General Fibonacci Identity (3 revisions)
- Signed Lah numbers (3 revisions)
- Q-Bessel functions (3 revisions)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (3 revisions)
- Taylor series for Gudermannian (2 revisions)
- Ramanujan tau is multiplicative (2 revisions)
- 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 (2 revisions)
- Weierstrass zeta (2 revisions)
- E(2,1)(-z^2)=cos(z) (2 revisions)
- Orthogonality of Chebyshev U on (-1,1) (2 revisions)
- Fresnel S in terms of erf (2 revisions)
- The Euler-Mascheroni constant exists (2 revisions)
- E (0,1)(z)=1/(1-z) for abs(z) less than 1 (2 revisions)
- Product of Weierstrass elementary factors is entire (2 revisions)
- Airy zeta function at 2 (2 revisions)
- Relation between polygamma and Hurwitz zeta (2 revisions)
- Weierstrass factorization of cosh (2 revisions)
- Normal cdf (2 revisions)
- Elliptic gamma function (2 revisions)
- Riemann function is continuous (2 revisions)
- Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I (2 revisions)
- Q-Beta function (2 revisions)
- Q-Gamma at 1 (2 revisions)
- Logarithmic derivative of Jacobi theta 3 equals a sum of sines (2 revisions)
- Relationship between cosine, imaginary number, logarithm, and the golden ratio (2 revisions)
- F(2n+1)=F(n+1)^2+F(n)^2 (2 revisions)
- Catalan's constant using Dirichlet beta (2 revisions)
- Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1 (2 revisions)
- Cyclotomic polynomials (2 revisions)
- Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued) (2 revisions)
- 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 (2 revisions)
- Periodic function (2 revisions)
- Series for log(z) for Re(z) greater than 0 (2 revisions)
- Square numbers (2 revisions)
- Alexander operator (2 revisions)
- Lerch transcendent polylogarithm (2 revisions)
- Bessel (2 revisions - redirect page)
- Relationship between Weber function 2 and Struve function 2 (2 revisions)
- Paper:Maruti Ram Murty/The Fibonacci Zeta Function (2 revisions)
- Integral representation of Struve function (2 revisions)
- Boole polynomials (2 revisions)
- Taylor series for sinh (2 revisions)
- Log(z)=log(10)log 10(z) (2 revisions)
- Ramanujan tau of a power of a prime (2 revisions)
- Gauss' formula for gamma function (2 revisions)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (2 revisions)
- Relationship between cosine and hypergeometric 0F1 (2 revisions)
- Bolzano function is continuous (2 revisions)
- Orthogonality of Laguerre L (2 revisions)
- Paper folding constant (2 revisions)
- F(n+1)F(n-1)-F(n)^2=(-1)^n (2 revisions)
- (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 (2 revisions)
- Constant functions are elliptic functions (2 revisions)
- Laurent series of the Riemann zeta function (2 revisions)
- Denisyuk polynomials (2 revisions)
- Generating function for Laguerre L (2 revisions)
- Derivative of inverse error function (2 revisions)
- Relationship between Lerch transcendent and Lerch zeta (2 revisions)
- Integral of Bessel J for Re(nu) greater than -1 (2 revisions)
- Peters polynomials (2 revisions)
- Product representation of totient (2 revisions)
- Krawtchouk polynomial (2 revisions)
- Q-theta function (2 revisions)
- Arithmetic zeta function (2 revisions)
- Derivative of versine (2 revisions)
- Doubling identity for cosh (2) (2 revisions)
- Normalized sinc (2 revisions)
- Relationship between sech, inverse Gudermannian, and cos (2 revisions)
- Entire exponential integral (2 revisions)
- Polar coordinates (2 revisions)
- Sum of Lucas numbers (2 revisions)
- Log 10(z)=log(z)/log(10) (2 revisions)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (2 revisions)
- Relationship between cot, Gudermannian, and csch (2 revisions)
- Porter's constant (2 revisions)
- (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0 (2 revisions)
- Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 (2 revisions)
- Lefschetz zeta function (2 revisions)
- D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (2 revisions)
- Functional equation for Riemann xi (2 revisions)
- Logarithm (multivalued) of product is a sum of logarithms (multivalued) (2 revisions)
- Vercosine (2 revisions)
- Bell numbers (2 revisions)
- Hankel H (2) in terms of csc and Bessel J (2 revisions)
- Hypergeometric 0F3 (2 revisions)
- Limiting value of Fresnel C (2 revisions)
- Derivative of zeta at -1 (2 revisions)
- Weierstrass factorization of sinh (2 revisions)
- Meromorphic continuation of q-exponential E sub q (2 revisions)
- Norton's constant (2 revisions)
- Sum of cosh and sinh (2 revisions)
- Q-Gaussian distribution (2 revisions)
- 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) (2 revisions)
- Hahn-Exton q-Bessel (2 revisions)
- Euler-Jackson q-difference operator (2 revisions)
- Irrational (2 revisions)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (2 revisions)
- Generating relation for Bateman F (2 revisions)
- Bell polynomial (2 revisions)
- NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (2 revisions)
- Hypergeometric 1F0 (2 revisions)
- Paper:Harry Bateman/Some Properties of a certain Set of Polynomials (2 revisions)
- Euler totient is multiplicative (2 revisions)
- Alternating sum over bottom of binomial coefficient with top fixed equals 0 (2 revisions)
- Limiting value of Fresnel S (2 revisions)
- Quotient rule (2 revisions)
- Twin prime constant (2 revisions)
- Artin constant (2 revisions)
- Binomial coefficient (n choose n) equals 1 (2 revisions)
- Paper:R. M. Corless/On the Lambert W function (2 revisions)
- Q-Hermite polynomial (2 revisions)
- Darboux function is continuous (2 revisions)
- Gelfond-Schneider constant is transcendental (2 revisions)
- B(x,y+1)=(y/(x+y))B(x,y) (2 revisions)
- Hahn polynomial (2 revisions)
- P-adic zeta function (2 revisions)
- Relationship between tan and tanh (2 revisions)
- Khinchin's constant (2 revisions)
- Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (2 revisions)
- Functional equation for Riemann zeta with cosine (2 revisions)
- Derivative is a linear operator (2 revisions)
- Reciprocal zeta function (2 revisions)
- Bernardi operator (2 revisions)
- Relationship between Meixner polynomials and Charlier polynomials (2 revisions)
- Series for polygamma in terms of Riemann zeta (2 revisions)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (2 revisions)
- L(n)=F(n+1)+F(n-1) (2 revisions)
- T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (2 revisions)
- Anger derivative recurrence (2 revisions)
- Tanh of a sum (2 revisions)
- Quotient rule for derivatives (2 revisions)
- Two-dimensional Laplace transform (2 revisions)
- H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (2 revisions)
- Binomial series (2 revisions)
- Erdős-Borwein Constant is irrational (2 revisions)
- Paper:Richard Askey/The q-Gamma and q-Beta functions (2 revisions)
- Böhmer S (2 revisions)
- Sum of divisors functions written in terms of partition function (2 revisions)
- 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z) (2 revisions)
- B(x,y+1)=(y/x)B(x+1,y) (2 revisions)
- Relationship between Bessel Y sub n and Bessel Y sub -n (2 revisions)
- Halving identity for cosh (2 revisions)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (2 revisions)
- Padovan polynomials (2 revisions)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (2 revisions)
- Prime number theorem, logarithmic integral (2 revisions)
- (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (2 revisions)
- Functions named after Carl Gustav Jacob Jacobi (2 revisions)
- Logarithm at -i (2 revisions)
- Recurrence relation for Struve fuction (2 revisions)
- Gieseking constant (2 revisions)
- Matsumoto zeta function (2 revisions)
- Narumi polynomials (2 revisions)
- Integral of Bessel J for nu=n+1 (2 revisions)
- Pidduck polynomial (2 revisions)
- Pythagorean identity for coth and csch (2 revisions)
- Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 (2 revisions)
- Two-sided inequality for e^(x^2) integral from x to infinity e^(-t^2) dt for non-negative real x (2 revisions)
- Mertens function (2 revisions)
- Humbert polynomials (2 revisions)
- Erf of conjugate is conjugate of erf (2 revisions)
- Riemann zeta at even integers (2 revisions)
- C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 (2 revisions)
- Sum of even indexed Fibonacci numbers (2 revisions)
- Pell constant is irrational (2 revisions)
- Libera operator (2 revisions)
- Q-number of a negative (2 revisions)
- Derivative of Bessel J with respect to its order (2 revisions)
- Arcsin cdf (2 revisions)
- Logarithm at i (2 revisions)
- Natural number (2 revisions)
- Relationship between logarithm and Mangoldt (2 revisions)
- Pincherle polynomials (2 revisions)
- 1/q-number as a q-number (2 revisions)
- T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (2 revisions)
- Log((1+z)/(1-z)) as continued fraction (2 revisions)
- Ramanujan constant (2 revisions)
- H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (2 revisions)
- Relationship between cosh, inverse Gudermannian, and sec (2 revisions)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (2 revisions)
- Laplace cdf (2 revisions)
- Derivative of cosine integral (2 revisions)
- Mott polynomial (2 revisions)
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (2 revisions)
- Cauchy pdf (2 revisions)
- Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m (2 revisions)
- Totient (2 revisions - redirect page)
- Logarithm at minus 1 (2 revisions)
- Dirichlet function (2 revisions)
- Nested radical constant (2 revisions)
- Paper:James Whitbread Lee Glaisher/On the Sums of the Inverse Powers of the Prime Numbers (2 revisions)
- Riemann Siegel theta function (2 revisions)
- Book:W.N. Bailey/Generalized Hypergeometric Series (2 revisions)
- Sierpiński constant (2 revisions)
- 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) (2 revisions)
- Logarithm of quotient of Jacobi theta 3 equals a sum of sines (2 revisions)
- Dickman–de Bruijn function (2 revisions)
- Hurwitz zeta absolute convergence (2 revisions)
- Relationship between sinh, inverse Gudermannian, and tan (2 revisions)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (2 revisions)
- F(-n)=(-1)^(n+1)F(n) (2 revisions)
- Sinh is odd (2 revisions)
- Laplace pdf (2 revisions)
- Q-Polygamma function (2 revisions)
- General Dirichlet series (2 revisions)
- Relationship between Chebyshev U and Gegenbauer C (2 revisions)
- Multiple gamma function (2 revisions)
- Relationship between csch, inverse Gudermannian, and cot (2 revisions)
- Paper:Charles Watkins Merrifield/The Sums of the Series of the Reciprocals of the Prime Numbers and of Their Powers (2 revisions)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (2 revisions)
- Euler numbers (2 revisions)
- Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition (2 revisions)
- Series for erf with exponential factored out (2 revisions)
- Sum rule for derivatives (2 revisions)
- Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4 (2 revisions)
- Touchard polynomial (2 revisions)
- Goh-Schmutz constant (2 revisions)
- Neumann polynomial (2 revisions)
- Hypergeometric 2F3 (2 revisions)
- Paper:Johann Cigler/q-Fibonacci Polynomials (2 revisions)
- Pythagorean identity for tanh and sech (2 revisions)
- Stirling polynomial (2 revisions)
- L n'(0)=-n (2 revisions)
- Faber F2 is continuous (2 revisions)
- Asymptotic formula for partition function (2 revisions)
- H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (2 revisions)
- Relationship between cosh and hypergeometric 0F1 (2 revisions)
- Relationship between sinh and hypergeometric 0F1 (2 revisions)
- Polygamma series representation (2 revisions)
- K-function (2 revisions)
- Relationship between Chebyshev U and hypergeometric 2F1 (2 revisions)
- Halving identity for tangent (3) (2 revisions)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (2 revisions)
- Period of tanh (2 revisions)
- -log(1-x) less than x/(1-x) (2 revisions)
- Sylvester's sequence (2 revisions)
- Bernoulli polynomial and Hurwitz zeta (2 revisions)
- Heaviside step function (2 revisions)
- Hypergeometric 3F2 (2 revisions)
- Book:George E. Andrews/Special Functions (2 revisions)
- Riemann function is almost nowhere differentiable (2 revisions)
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (2 revisions)
- Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition (2 revisions)
- Cosh of a sum (2 revisions)
- Takagi function is nowhere differentiable (2 revisions)
