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- 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (3 revisions)
- Contour integral representation of reciprocal gamma (3 revisions)
- Rodrigues formula for Meixner polynomial (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)
- Series for log(Riemann zeta) in terms of Mangoldt function (3 revisions)
- Logarithmic derivative of Riemann zeta in terms of Mangoldt function (3 revisions)
- Differential equation for Jacobi P (3 revisions)
- Orthogonality relation for cosine on (0,pi) (3 revisions)
- Partial derivative of beta function (3 revisions)
- Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1 (3 revisions)
- Signed Lah numbers (3 revisions)
- Generating function for partition function (3 revisions)
- 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) (3 revisions)
- Convergence of Hypergeometric pFq (3 revisions)
- Derivative of prime zeta (3 revisions)
- Logarithm of a quotient of Jacobi theta 4 equals a sum of sines (3 revisions)
- Integral representation of Struve function (3) (3 revisions)
- Relationship between Hurwitz zeta and gamma function (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 Weber function 1 and Struve function 1 (3 revisions)
- Absolute convergence of secant zeta function (3 revisions)
- Chaitin's constant (3 revisions)
- Sister Celine's polynomials (3 revisions)
- Logarithm of exponential (3 revisions)
- Mersenne numbers (3 revisions)
- T(n)=n(n+1)/2 (3 revisions)
- Van der Waerden function is continuous (3 revisions)
- Böhmer C (3 revisions)
- Relationship between exponential integral Ei, cosine integral, and sine integral (3 revisions)
- 2F1(1/2,1;3/2;-z^2)=arctan(z)/z (3 revisions)
- Derivative of Struve H0 (3 revisions)
- Q-Gamma at z+1 (3 revisions)
- Relationship between Airy Ai and modified Bessel K (3 revisions)
- Weierstrass factorization of cosine (3 revisions)
- Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt (3 revisions)
- Relationship between secant, Gudermannian, and cosh (3 revisions)
- Log a(b)=1/log b(a) (3 revisions)
- Sum of squares of Fibonacci numbers (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)
- Logarithm of product is a sum of logarithms (3 revisions)
- Integral representation of polygamma 2 (3 revisions)
- Relationship between incomplete beta and hypergeometric 2F1 (3 revisions)
- Riccati-Bessel S (3 revisions)
- Faddeeva function (3 revisions)
- Derivative of arccos (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 Airy Bi and modified Bessel I (3 revisions)
- Relationship between Weber function and Anger function (3 revisions)
- Hypergeometric 1F2 (3 revisions)
- Paper:Harvey Dubner/Factorial and Primorial Primes (3 revisions)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (3 revisions)
- Relationship between spherical Bessel y and cosine (3 revisions)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (3 revisions)
- Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 (3 revisions)
- Bessel J in terms of Bessel-Clifford (3 revisions)
- Q-Binomial coefficient (3 revisions)
- Q-exponential e sub 1/q (3 revisions)
- Derivative of arccosh (3 revisions)
- Modular form (3 revisions)
- Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition (3 revisions)
- Relationship between sech and sec (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)
- Exponential e in terms of basic hypergeometric phi (3 revisions)
- Integral of inverse erf from 0 to 1 (3 revisions)
- Relationship between cot and coth (3 revisions)
- L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) (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)
- Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm (3 revisions)
- Fermat numbers (3 revisions)
- Derivative of arccot (3 revisions)
- Series for log(z+a) for positive a and Re(z) greater than -a (3 revisions)
- Lower incomplete gamma (3 revisions)
- Halving identity for tangent (1) (3 revisions)
- Relationship between arcsin and arccsc (3 revisions)
- Legendre chi in terms of polylogarithm (3 revisions)
- Dawson D- (3 revisions)
- Riemann zeta as contour integral (3 revisions)
- Havercosine (3 revisions)
- Integral of log of inverse erf from 0 to 1 (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)
- Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 (3 revisions)
- Minkowski question mark (3 revisions)
- Antiderivative of inverse error function (3 revisions)
- Derivative of arccoth (3 revisions)
- Asymptotic behavior of Sievert integral (3 revisions)
- Lucas (3 revisions)
- Digamma at z+n (3 revisions)
- Relationship between sine, Gudermannian, and tanh (3 revisions)
- Sum of values of sinc (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)
- Relationship between tangent, Gudermannian, and sinh (3 revisions)
- Dickson polynomial (3 revisions)
- Q-Euler formula for E sub q (3 revisions)
- E(1,1)(z)=exp(z) (3 revisions)
- Paper:Tom H. Koornwinder/q-Special functions, a tutorial (3 revisions)
- Integration by parts (3 revisions)
- Riemann-Siegel Z (3 revisions)
- Gamma function written as a limit of a factorial, exponential, and a rising factorial (3 revisions)
- Barnes zeta function (4 revisions)
- Relationship between sine, imaginary number, logarithm, and the golden ratio (4 revisions)
- Dirichlet series (4 revisions)
- Q-derivative power rule (4 revisions)
- Antiderivative of arccos (4 revisions)
- Logarithm diverges to negative infinity at 0 from right (4 revisions)
- Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines (4 revisions)
- Stieltjes constants (4 revisions)
- Bohr-Mollerup theorem (4 revisions)
- U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (4 revisions)
- Cellérier function (4 revisions)
- Generalized q-Bessel (4 revisions)
- Bernstein B (4 revisions)
- Sum over bottom of binomial coefficient with top fixed equals 2^n (4 revisions)
- Relationship between csc, Gudermannian, and coth (4 revisions)
- 1Phi0(a;;z) as infinite product (4 revisions)
- Relationship between tanh and tan (4 revisions)
- Stirling numbers of the second kind (4 revisions)
- Relationship between Sievert integral and exponential integral E (4 revisions)
- Relationship between logarithm and positive integer exponents (4 revisions)
- Relationship between Bessel I sub -1/2 and cosh (4 revisions)
- Relationship between cosh and cos (4 revisions)
- Dedekind zeta function (4 revisions)
- Binomial coefficient (n choose 0) equals 1 (4 revisions)
- Pochhammer symbol with non-negative integer subscript (4 revisions)
- Chebyshev psi function (4 revisions)
- 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) (4 revisions)
- Limit of quotient of consecutive Fibonacci numbers (4 revisions)
- Weierstrass elliptic (4 revisions)
- Derivative of arcsinh (4 revisions)
- E is limit of (1+1/n)^n (4 revisions)
- Paper:Edmund Landau/Sur la série des inverse de nombres de Fibonacci (4 revisions)
- Logarithm of a quotient is a difference of logarithms (4 revisions)
- Relationship between csch and csc (4 revisions)
- 2F1(1,1;2;z)=-log(1-z)/z (4 revisions)
- Catalan's constant using Legendre chi (4 revisions)
- Relationship between Weber function 0 and Struve function 0 (4 revisions)
- Constant multiple rule for derivatives (4 revisions)
- Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta (4 revisions)
- Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications (4 revisions)
- Relationship between Bessel I sub 1/2 and sinh (4 revisions)
- Chain rule for derivatives (4 revisions)
- Sinhc (4 revisions)
- Series for log(riemann zeta) over primes (4 revisions)
- Book:Aleksandar Ivić/The Riemann Zeta-Function (4 revisions)
- Book:Michael Wilensky/Ueber Besselsche Funktionen (4 revisions)
- Floor (4 revisions)
- X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 (4 revisions)
- Erdős-Borwein Constant (4 revisions)
- Exponential of logarithm (4 revisions)
- Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 (4 revisions)
- Digamma at 1 (4 revisions)
- Sum of Fibonacci numbers (4 revisions)
- Genocchi numbers (4 revisions)
- Matrix exponential (4 revisions)
- N^2=T(n)+T(n-1) (4 revisions)
- Hypergeometric 1F1 (4 revisions)
- Value of Ai'(0) (4 revisions)
- Soldner's Constant (4 revisions)
- Cotangent zeta function (4 revisions)
- Modified Struve function (4 revisions)
- Trigamma (4 revisions)
- Pell constant (4 revisions)
- Ramanujan theta function (4 revisions)
- T(n+1)=T(n)+n+1 (4 revisions)
- Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x) (4 revisions)
- Polygamma multiplication formula (4 revisions)
- Falling factorial (4 revisions)
- Series for log(z) for absolute value of (z-1) less than 1 (4 revisions)
- Loggamma (4 revisions)
- Digamma at n+1 (4 revisions)
- Jackson q-Bessel (2) (4 revisions)
- (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) (4 revisions)
- Prime number theorem, pi and x/log(x) (4 revisions)
- McCarthy function (4 revisions)
- Sum of totient equals z/((1-z) squared) (4 revisions)
- Hypergeometric 2F0 (4 revisions)
- Value of Anger at 0 (4 revisions)
- Squares of theta relation for Jacobi theta 2 and Jacobi theta 4 (4 revisions)
- Coth of a sum (4 revisions)
- Antiderivative of hyperbolic cosecant (4 revisions)
- E^x is greater than 1+x for nonzero real x (4 revisions)
- Barnes G at positive integer (4 revisions)
- Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 (4 revisions)
- Derivative of Bessel Y with respect to its order (4 revisions)
- Imaginary number (4 revisions)
- Book:Johann Heinrich Graf/Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale (4 revisions)
- Bessel polynomial generalized hypergeometric (4 revisions)
- E^x is less than 1/(1-x) for nonzero real x less than 1 (4 revisions)
- Relationship between Anger function and Weber function (4 revisions)
- Riemann zeta as integral of monomial divided by an exponential (4 revisions)
- Binet's formula (4 revisions)
- Real and imaginary parts of log (4 revisions)
- Relationship between coth and cot (4 revisions)
- Anger three-term recurrence (4 revisions)
- Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines (4 revisions)
- Orthogonality of Chebyshev T on (-1,1) (4 revisions)
- Incomplete Elliptic E (4 revisions)
- Abel p (4 revisions)
- Antiderivative of sech (4 revisions)
- Lucas numbers (5 revisions)
- Bessel polynomial in terms of Bessel functions (5 revisions)
- Derivative of coth (5 revisions)
- Relationship between tanh, inverse Gudermannian, and sin (5 revisions)
- Derivative of arcsec (5 revisions)
- Taylor series (5 revisions)
- Paper:Daniel S. Moak/The q-gamma function for q greater than 1 (5 revisions)
- Meissel-Mertens constant (5 revisions)
- Value of polygamma at 1 (5 revisions)
- Difference of cosh and sinh (5 revisions)
- Antiderivative of tanh (5 revisions)
- E is irrational (5 revisions)
- Product representation of q-exponential E sub 1/q (5 revisions)
- Rising factorial (5 revisions)
- Value of polygamma at 1/2 (5 revisions)
- Antiderivative of arcsin (5 revisions)
- Dirichlet L-function (5 revisions)
- Lerch zeta function (5 revisions)
- Paper:Matilde Lalín/Secant zeta functions (5 revisions)
- Brun's constant (5 revisions)
- Derivative of Li 2(-1/x) (5 revisions)
- Gamma(n+1)=n! (5 revisions)
- Bessel at -n-1/2 in terms of Bessel polynomial (5 revisions)
- E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936 (5 revisions)
- Transcendental (5 revisions)
- Book:Edmund Taylor Whittaker/A course of modern analysis/Third edition (5 revisions)
- Petr function (5 revisions)
- Relationship between cosine, Gudermannian, and sech (5 revisions)
- Li2(z)=zPhi(z,2,1) (5 revisions)
- Depreciated trigonometric functions footer (5 revisions)
- Schwarz function (5 revisions)
- Epstein zeta function (5 revisions)
- Buchstab function (5 revisions)
- Artin-Mazur zeta function (5 revisions)
- Legendre's constant (5 revisions)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 (5 revisions)
- Li 2(1)=pi^2/6 (5 revisions)
- Clausen cosine (5 revisions)
- Relationship between the exponential integral and upper incomplete gamma function (5 revisions)
