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- Gamma(z+1)=zGamma(z) (3 categories)
- Taylor series for error function (3 categories)
- Integral of Bessel J for nu=1 (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)
- Integral representation of Struve function (2) (2 categories)
- Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1 (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)
- The Euler-Mascheroni constant exists (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)
- Derivative of Li 2(-1/x) (2 categories)
- 1Phi0(a;;z) as infinite product (2 categories)
- Derivative of arcsec (2 categories)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (2 categories)
- Derivative of cosine integral (2 categories)
- Value of polygamma at positive integer (2 categories)
- Derivative of sech (2 categories)
- Antiderivative of arccos (2 categories)
- Derivative of versine (2 categories)
- Weierstrass function is continuous (2 categories)
- Antiderivative of hyperbolic cosecant (2 categories)
- Differential equation for Jacobi P (2 categories)
- X less than -log(1-x) (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)
- 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)
- Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 (2 categories)
- Halving identity for tangent (2) (2 categories)
- Sum of cosh and sinh (2 categories)
- Haversine (2 categories)
- Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 (2 categories)
- T(n+1)=T(n)+n+1 (2 categories)
- Taylor series for Gudermannian (2 categories)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (2 categories)
- Integral representation of Struve function (3) (2 categories)
- Real and imaginary parts of log (2 categories)
- L(-n)=(-1)^nL(n) (2 categories)
- Reciprocal of i (2 categories)
- Relationship between Airy Bi and modified Bessel I (2 categories)
- Relationship between Bessel Y sub n and Bessel Y sub -n (2 categories)
- Li2(z)=zPhi(z,2,1) (2 categories)
- Relationship between Li 2(1),Li 2(-1), and pi (2 categories)
- Limit of q-exponential E sub 1/q for 0 less than q less than 1 (2 categories)
- Relationship between arcsin and arccsc (2 categories)
- Log(1+z) as continued fraction (2 categories)
- Relationship between cosine and hypergeometric 0F1 (2 categories)
- Log e(z)=log(z) (2 categories)
- Relationship between csch and csc (2 categories)
- Logarithm at minus 1 (2 categories)
- Relationship between logarithm and positive integer exponents (2 categories)
- Logarithm of product is a sum of logarithms (2 categories)
- Relationship between sine, Gudermannian, and tanh (2 categories)
- Logarithmic derivative of Riemann zeta in terms of Mangoldt function (2 categories)
- Relationship between tan and tanh (2 categories)
- Meromorphic continuation of q-exponential E sub q (2 categories)
- N^2=T(n)+T(n-1) (2 categories)
- Series for log(riemann zeta) over primes (2 categories)
- Orthogonality relation for cosine on (0,pi) (2 categories)
- Pell constant is irrational (2 categories)
- Polygamma reflection formula (2 categories)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (2 categories)
- Product of Weierstrass elementary factors is entire (2 categories)
- Integral of Bessel J for nu=n+1 (2 categories)
- Derivative is a linear operator (2 categories)
- The Petr function is continuous (2 categories)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 (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)
- Derivative of arcsin (2 categories)
- Derivative of cotangent (2 categories)
- Derivative of sine (2 categories)
- Weierstrass elementary factors inequality (2 categories)
- Antiderivative of arccosh (2 categories)
- Derivative of zeta at -1 (2 categories)
- Weierstrass function is nowhere differentiable (2 categories)
- Antiderivative of inverse error function (2 categories)
- X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 (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)
- Generating function for Laguerre L (2 categories)
- C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x) (2 categories)
- Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 (2 categories)
- Halving identity for tangent (3) (2 categories)
- Closed form for partition function with sinh (2 categories)
- Sum of totient equals z/((1-z) squared) (2 categories)
- Hyperfactorial in terms of K-function (2 categories)
- Cosh is even (2 categories)
- T(n+1)^2-T(n)^2=(n+1)^3 (2 categories)
- Coth of a sum (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)
- Integral representation of polygamma 2 (2 categories)
- Q-Gamma at 1 (2 categories)
- Q-derivative of q-Cosine (2 categories)
- L(n)=F(n+1)+F(n-1) (2 categories)
- Lambert W (2 categories)
- Relationship between Anger function and Bessel J (2 categories)
- Relationship between Chebyshev T and Gegenbauer C (2 categories)
- Li 2(1)=pi^2/6 (2 categories)
- Relationship between Meixner polynomials and Charlier polynomials (2 categories)
- Limit of quotient of consecutive Fibonacci numbers (2 categories)
- Relationship between arctan and arccot (2 categories)
- Log(x) less than or equal to n(x^(1/n)-1) (2 categories)
- Relationship between cot, Gudermannian, and csch (2 categories)
- Relationship between dilogarithm and log(1-z)/z (2 categories)
- Relationship between logarithmic integral and exponential integral (2 categories)
- Logarithm of quotient of Jacobi theta 1 equals the log of a quotient of sines + a sum of sines (2 categories)
- Relationship between sine, imaginary number, logarithm, and the golden ratio (2 categories)
- Logarithmic derivative of Riemann zeta in terms of series over primes (2 categories)
- Relationship between tangent, Gudermannian, and sinh (2 categories)
- Riemann-Landau xi is even (2 categories)
- Riemann zeta as contour integral (2 categories)
- Series for log(z) for Re(z) greater than 0 (2 categories)
- Nth derivative of logarithm (2 categories)
- Sinh is odd (2 categories)
- Period of cosh (2 categories)
- Polygamma series representation (2 categories)
- 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) (2 categories)
- Product representation of q-exponential E sub 1/q (2 categories)
- Integral of inverse erf from 0 to 1 (2 categories)
- Derivative of Bessel-Clifford (2 categories)
- The Petr function is nowhere differentiable (2 categories)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (2 categories)
- Derivative of Struve H0 (2 categories)
- 2F1(1,1;2;z)=-log(1-z)/z (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)
- Van der Waerden function is continuous (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)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (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)
- Generating function for partition function (2 categories)
- Closed formula for physicist's Hermite polynomials (2 categories)
- Sum of divisors functions written in terms of partition function (2 categories)
- Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 (2 categories)
- Cosh of a sum (2 categories)
- T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (2 categories)
- Darboux function is nowhere differentiable (2 categories)
- Taylor series for sinh (2 categories)
- (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x)) (2 categories)
- Integral representation of polygamma for Re(z) greater than 0 (2 categories)
- Q-Gamma at z+1 (2 categories)
- Q-derivative of q-Sine (2 categories)
- L(n)^2-5F(n)^2=4(-1)^n (2 categories)
- Recurrence relation for Struve fuction (2 categories)
- Relationship between Bessel-Clifford and hypergeometric 0F1 (2 categories)
- Relationship between Chebyshev T and hypergeometric 2F1 (2 categories)
- Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (2 categories)
- Relationship between Scorer Gi and Airy functions (2 categories)
- Limit of x^a log(x)=0 (2 categories)
- Relationship between cos and cosh (2 categories)
- Log(x) less than or equal to x-1 (2 categories)
- Relationship between cot and coth (2 categories)
- Relationship between exponential integral Ei, cosine integral, and sine integral (2 categories)
- Logarithm diverges to negative infinity at 0 from right (2 categories)
- Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta (2 categories)
- Logarithm of quotient of Jacobi theta 2 equals the log of a quotient of cosines + a sum of sines (2 categories)
- Relationship between sine and hypergeometric 0F1 (2 categories)
- Relationship between tanh, inverse Gudermannian, and sin (2 categories)
- Riemann zeta as integral of monomial divided by an exponential (2 categories)
- Series for log(z) for Re(z) greater than 1/2 (2 categories)
- Sinh of a sum (2 categories)
- Sqrt(1-z^2)2F1(1,1;3/2;z^2)=arcsin(z)/z (2 categories)
- Period of sinh (2 categories)
- 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) (2 categories)
- Product representation of totient (2 categories)
- Integral of log of inverse erf from 0 to 1 (2 categories)
- Derivative of Bessel J with respect to its order (2 categories)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (2 categories)
- Derivative of arccos (2 categories)
- 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z (2 categories)
- Derivative of arctan (2 categories)
- Value of Ai'(0) (2 categories)
- Abs(log(1+z)) less than or equal to -log(1-abs(z)) (2 categories)
- Derivative of erfi (2 categories)
- Van der Waerden function is nowhere differentiable (2 categories)
- Derivative of sinh (2 categories)
- Weierstrass factorization of cosh (2 categories)
- Antiderivative of arcsinh (2 categories)
- Devil's staircase is continuous (2 categories)
- Antiderivative of sine integral (2 categories)
- Digamma at 1/2 (2 categories)
- Z2F1(1,1;2,-z) equals log(1+z) (2 categories)
- Arccos as inverse cosine (2 categories)
- Dirichlet beta in terms of Lerch transcendent (2 categories)
- Doubling identity for cosh (3) (2 categories)
- E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936 (2 categories)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (2 categories)
