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- Gamma(z+1)=zGamma(z) (3 categories)
- Integral of Bessel J for nu=1 (3 categories)
- Taylor series for error function (3 categories)
- Derivative of prime zeta (3 categories)
- Derivative of the exponential function (3 categories)
- Fibonacci zeta in terms of a sum of binomial coefficients (3 categories)
- Recurrence relation for partition function with sum of divisors (2 categories)
- Relationship between Bessel I sub -1/2 and cosh (2 categories)
- Legendre chi in terms of polylogarithm (2 categories)
- Relationship between Chebyshev U and hypergeometric 2F1 (2 categories)
- Relationship between Sievert integral and exponential integral E (2 categories)
- Limiting value of Fresnel S (2 categories)
- Relationship between cosh and cos (2 categories)
- Log 10(z)=log(z)/log(10) (2 categories)
- Relationship between coth and cot (2 categories)
- Logarithm (multivalued) of product is a sum of logarithms (multivalued) (2 categories)
- Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm (2 categories)
- Logarithm of a complex number (2 categories)
- Relationship between secant, Gudermannian, and cosh (2 categories)
- Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines (2 categories)
- Relationship between sinh and hypergeometric 0F1 (2 categories)
- Relationship between the Fransén–Robinson constant, e, pi, and logarithm (2 categories)
- McCarthy function is nowhere differentiable (2 categories)
- Rodrigues formula for Meixner polynomial (2 categories)
- Series for log(z+a) for positive a and Re(z) greater than -a (2 categories)
- Orthogonality of Chebyshev T on (-1,1) (2 categories)
- Square of i (2 categories)
- Pochhammer symbol with non-negative integer subscript (2 categories)
- Integral of Bessel J for Re(nu) greater than -1 (2 categories)
- Pythagorean identity for coth and csch (2 categories)
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (2 categories)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (2 categories)
- Q-difference equation for q-exponential E sub 1/q (2 categories)
- Q-number of a negative (2 categories)
- Ramanujan tau inequality (2 categories)
- Knopp function is continuous (2 categories)
- L n'(0)=-n (2 categories)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (2 categories)
- Z coth(z) = 2z/(e^(2z)-1) + z (2 categories)
- Derivative of cosine integral (2 categories)
- Derivative of sech (2 categories)
- Antiderivative of arccos (2 categories)
- Derivative of versine (2 categories)
- Antiderivative of hyperbolic cosecant (2 categories)
- Differential equation for Jacobi P (2 categories)
- Apéry's constant is irrational (2 categories)
- E(2,1)(-z^2)=cos(z) (2 categories)
- 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 categories)
- E^x is less than 1/(1-x) for nonzero real x less than 1 (2 categories)
- Barnes G at positive integer (2 categories)
- Euler's formula (2 categories)
- Euler totient is multiplicative (2 categories)
- Beta in terms of gamma (2 categories)
- Exsecant (2 categories)
- Binomial series (2 categories)
- Functional equation for Riemann zeta (2 categories)
- Generating function for Hermite (physicist) polynomials (2 categories)
- Sum of odd indexed Fibonacci numbers (2 categories)
- C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 (2 categories)
- Champernowne constant is transcendental (2 categories)
- Halving identity for tangent (2) (2 categories)
- Haversine (2 categories)
- Taylor series of log(1-z) (2 categories)
- Thomae function is discontinuous at rationals (2 categories)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (2 categories)
- Versine (2 categories)
- 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) (2 categories)
- Weierstrass factorization of sine (2 categories)
- Derivative of Li 2(-1/x) (2 categories)
- 1Phi0(a;;z) as infinite product (2 categories)
- X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 (2 categories)
- Derivative of arcsec (2 categories)
- Recurrence relation of exponential integral E (2 categories)
- Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1 (2 categories)
- Relationship between Bessel I sub 1/2 and sinh (2 categories)
- Relationship between Hurwitz zeta and gamma function (2 categories)
- Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m (2 categories)
- Relationship between Struve function and hypergeometric pFq (2 categories)
- Relationship between cosh and hypergeometric 0F1 (2 categories)
- Log 10(z)=log 10(e)log(z) (2 categories)
- Relationship between coth and csch (2 categories)
- Relationship between logarithm (multivalued) and logarithm (2 categories)
- Logarithm of a quotient is a difference of logarithms (2 categories)
- Relationship between sech, inverse Gudermannian, and cos (2 categories)
- Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines (2 categories)
- Relationship between sinh and sin (2 categories)
- Relationship between the Gegenbauer C polynomials and the Jacobi P polynomials (2 categories)
- Riemann function is almost nowhere differentiable (2 categories)
- Möbius function is multiplicative (2 categories)
- Series for polygamma in terms of Riemann zeta (2 categories)
- Orthogonality of Chebyshev U on (-1,1) (2 categories)
- Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 (2 categories)
- Partial derivative of beta function (2 categories)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (2 categories)
- Prime number theorem, logarithmic integral (2 categories)
- Pythagorean identity for sin and cos (2 categories)
- Integral representation of Airy Ai (2 categories)
- Q-Euler formula for E sub q (2 categories)
- Q-difference equation for q-exponential E sub q (2 categories)
- Q-number when a=n is a natural number (2 categories)
- Ramanujan tau is multiplicative (2 categories)
- Knopp function is nowhere differentiable (2 categories)
- Reciprocal gamma is entire (2 categories)
- L n'(x)=-Sum L k(x) (2 categories)
- Derivative of arcsin (2 categories)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (2 categories)
- Derivative of cotangent (2 categories)
- Derivative of sine (2 categories)
- Antiderivative of arccosh (2 categories)
- Derivative of zeta at -1 (2 categories)
- Antiderivative of inverse error function (2 categories)
- Doubling identity for cosh (1) (2 categories)
- E(2,1)(z)=cosh(sqrt(z)) (2 categories)
- B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (2 categories)
- E (0,1)(z)=1/(1-z) for abs(z) less than 1 (2 categories)
- Barnes G at z+1 in terms of Barnes G and gamma (2 categories)
- Bessel at -n-1/2 in terms of Bessel polynomial (2 categories)
- Exponential (2 categories)
- Beta in terms of power of t over power of (1+t) (2 categories)
- Binomial theorem (2 categories)
- Faber F1 is continuous (2 categories)
- Functional equation for Riemann zeta with cosine (2 categories)
- Gamma function written as infinite product (2 categories)
- Sum of Fibonacci numbers (2 categories)
- Generating function for Laguerre L (2 categories)
- Sum of reciprocal Pochhammer symbols of a fixed exponent (2 categories)
- C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x) (2 categories)
- Symmetry relation of exponential integral E (2 categories)
- Takagi function is continuous (2 categories)
- Halving identity for tangent (3) (2 categories)
- Taylor series for Fresnel C (2 categories)
- Closed form for partition function with sinh (2 categories)
- Taylor series of sine (2 categories)
- Hyperfactorial in terms of K-function (2 categories)
- Three-term recurrence for Bateman F (2 categories)
- Cosh is even (2 categories)
- U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (2 categories)
- Coth of a sum (2 categories)
- Value of derivative of trigamma at positive integer plus 1/2 (2 categories)
- Darboux function is continuous (2 categories)
- (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x) (2 categories)
- Wallis product (2 categories)
- Derivative is a linear operator (2 categories)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 (2 categories)
- Weierstrass factorization of sinh (2 categories)
- Derivative of Riemann zeta (2 categories)
- 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) (2 categories)
- X/(1+x) less than log(1+x) (2 categories)
- Relation between polygamma and Hurwitz zeta (2 categories)
- Laurent series of the Riemann zeta function (2 categories)
- Relationship between Bessel J and hypergeometric 0F1 (2 categories)
- Lerch transcendent polylogarithm (2 categories)
- Relationship between Lerch transcendent and Lerch zeta (2 categories)
- Relationship between Weber function 0 and Struve function 0 (2 categories)
- Log((1+z)/(1-z)) as continued fraction (2 categories)
- Relationship between cosine, Gudermannian, and sech (2 categories)
- Log a(b)=1/log b(a) (2 categories)
- Relationship between csc, Gudermannian, and coth (2 categories)
- Logarithm at -i (2 categories)
- Relationship between logarithm (multivalued) and positive integer exponents (2 categories)
- Logarithm of a quotient of Jacobi theta 4 equals a sum of sines (2 categories)
- Relationship between sech and sec (2 categories)
- Logarithmic derivative of Jacobi theta 3 equals a sum of sines (2 categories)
- Relationship between spherical Bessel j and sine (2 categories)
- Relationship between the exponential integral and upper incomplete gamma function (2 categories)
- Meissel-Mertens constant in terms of the Euler-Mascheroni constant (2 categories)
- Riemann function is continuous (2 categories)
- Schwarz function is continuous (2 categories)
- NC n^(lambda)(x)=(n-1+2lambda)xC (n-1)^(lambda)(x)-2lambda(1-x^2)C (n-2)^(lambda-1)(x) (2 categories)
- Series for erf with exponential factored out (2 categories)
- Series for q-sin sub q (2 categories)
- Orthogonality of Gegenbauer C on (-1,1) (2 categories)
- Sine (2 categories)
- Polygamma multiplication formula (2 categories)
- Integral from a to a (2 categories)
- Prime number theorem, pi and x/log(x) (2 categories)
- Integral of Bessel J for nu=2n (2 categories)
- Pythagorean identity for sinh and cosh (2 categories)
- Integral representation of Struve function (2 categories)
- Q-Euler formula for e sub q (2 categories)
- Ramanujan tau of a power of a prime (2 categories)
- Reciprocal gamma written as an infinite product (2 categories)
- L n(0)=1 (2 categories)
- XL n'(x)=nL n(x)-n L (n-1)(x) (2 categories)
- Derivative of arcsinh (2 categories)
- Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z)) (2 categories)
- Derivative of coth (2 categories)
- Airy zeta function at 2 (2 categories)
- Derivative of sine integral (2 categories)
- Antiderivative of arcsin (2 categories)
- Antiderivative of sech (2 categories)
- Digamma at 1 (2 categories)
- Doubling identity for cosh (2) (2 categories)
- E(m)=(pi/2)2F1(-1/2,1/2;1;m) (2 categories)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (2 categories)
- E is irrational (2 categories)
- Euler E generating function (2 categories)
- Bessel at n+1/2 in terms of Bessel polynomial (2 categories)
- Beta in terms of sine and cosine (2 categories)
- F(-n)=(-1)^(n+1)F(n) (2 categories)
- Bohr-Mollerup theorem (2 categories)
- Faber F1 is nowhere differentiable (2 categories)
- Fresnel C in terms of erf (2 categories)
- Squares of theta relation for Jacobi theta 2 and Jacobi theta 4 (2 categories)
- Sum of Lucas numbers (2 categories)
- Generating function for partition function (2 categories)
- Sum of squares of Fibonacci numbers (2 categories)
- T(n)^2=T(T(n))+T(T(n)-1) (2 categories)
- Takagi function is nowhere differentiable (2 categories)
- Taylor series for Fresnel S (2 categories)
- Closed formula for physicist's Hermite polynomials (2 categories)
- Taylor series of the exponential function (2 categories)
- Cosh of a sum (2 categories)
- U n(x)=Sum (-1)^k n!/((2k+1)!(n-2k-1)!)(1-x^2)^(k+1/2)x^(n-2k-1) (2 categories)
- Value of polygamma at 1/2 (2 categories)
- Darboux function is nowhere differentiable (2 categories)
- (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (2 categories)
- Weber function (2 categories)
- Derivative of Bessel-Clifford (2 categories)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (2 categories)
- Weierstrass factorization theorem (2 categories)
- Derivative of Struve H0 (2 categories)
- 2F1(1,1;2;z)=-log(1-z)/z (2 categories)
- L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) (2 categories)
- Relationship between Airy Ai and modified Bessel K (2 categories)
- Relationship between Bessel J sub n and Bessel J sub -n (2 categories)
- Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x) (2 categories)
- Limit of log(x)/x^a=0 (2 categories)
- Relationship between Weber function 1 and Struve function 1 (2 categories)
- Log(1+x) less than x (2 categories)
- Relationship between cosine, imaginary number, logarithm, and the golden ratio (2 categories)
- Log base a in terms of logarithm base b (2 categories)
- Relationship between csch, inverse Gudermannian, and cot (2 categories)
- Logarithm at i (2 categories)
- Relationship between logarithm and Mangoldt (2 categories)
- Relationship between sin and sinh (2 categories)
- Logarithmic derivative of Jacobi theta 4 equals a sum of sines (2 categories)
- Relationship between spherical Bessel y and cosine (2 categories)
- Matrix e^A=limit of (I+A/s)^s (2 categories)
- Schwarz function is nowhere differentiable on a dense subset (2 categories)
- NC n^(lambda)(x)=2lambda(xC (n-1)^(lambda+1)(x)-C (n-2)^(lambda+1)(x)) (2 categories)
- Series for log(Riemann zeta) in terms of Mangoldt function (2 categories)
- Orthogonality of Laguerre L (2 categories)
- Pi is irrational (2 categories)
- Identity written as a sum of Möbius functions (2 categories)
- Polygamma recurrence relation (2 categories)
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (2 categories)
- Integral of Bessel J for nu=2n+1 (2 categories)
- Pythagorean identity for tanh and sech (2 categories)
- Integral representation of Struve function (2) (2 categories)
