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- Logarithmic derivative of Riemann zeta in terms of series over primes (2 categories)
- 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) (2 categories)
- Relationship between tangent, Gudermannian, and sinh (2 categories)
- Derivative of cosh (2 categories)
- Sum of divisors functions written in terms of partition function (2 categories)
- Absolute convergence of secant zeta function (2 categories)
- Riemann-Landau xi is even (2 categories)
- Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 (2 categories)
- Riemann zeta as contour integral (2 categories)
- T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (2 categories)
- Antiderivative of cosine integral (2 categories)
- Antiderivative of versine (2 categories)
- Series for log(z) for Re(z) greater than 0 (2 categories)
- Digamma at z+n (2 categories)
- Nth derivative of logarithm (2 categories)
- Taylor series for sinh (2 categories)
- Dirichlet function is nowhere continuous (2 categories)
- The Petr function is nowhere differentiable (2 categories)
- Sinh is odd (2 categories)
- Asymptotic behavior of Sievert integral (2 categories)
- E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0 (2 categories)
- B(x,y+1)=(y/x)B(x+1,y) (2 categories)
- Van der Waerden function is continuous (2 categories)
- Period of cosh (2 categories)
- Euler product for Riemann zeta (2 categories)
- Beta as improper integral (2 categories)
- Exponential integral Ei series (2 categories)
- Polygamma series representation (2 categories)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (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)
- F(n+1)F(n-1)-F(n)^2=(-1)^n (2 categories)
- Product representation of q-exponential E sub 1/q (2 categories)
- Integral of inverse erf from 0 to 1 (2 categories)
- Integral representation of polygamma for Re(z) greater than 0 (2 categories)
- Q-Gamma at z+1 (2 categories)
- Functional equation for Riemann xi (2 categories)
- Q-derivative of q-Sine (2 categories)
- Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 (2 categories)
- Catalan's identity (2 categories)
- L(n)^2-5F(n)^2=4(-1)^n (2 categories)
- H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (2 categories)
- Recurrence relation for Struve fuction (2 categories)
- Halving identity for tangent (1) (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)
- Hurwitz zeta absolute convergence (2 categories)
- Relationship between Scorer Gi and Airy functions (2 categories)
- Cosecant (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)
- D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (2 categories)
- (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0 (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)
- 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (2 categories)
- Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta (2 categories)
- Derivative of Legendre chi 2 (2 categories)
- Logarithm of quotient of Jacobi theta 2 equals the log of a quotient of cosines + a sum of sines (2 categories)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (2 categories)
- Relationship between sine and hypergeometric 0F1 (2 categories)
- Derivative of arccsc (2 categories)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (2 categories)
- Relationship between tanh, inverse Gudermannian, and sin (2 categories)
- Derivative of cosine (2 categories)
- Sum of even indexed Fibonacci numbers (2 categories)
- Derivative of secant (2 categories)
- Sum of values of sinc (2 categories)
- Riemann zeta as integral of monomial divided by an exponential (2 categories)
- Derivative of the logarithm (2 categories)
- T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n (2 categories)
- Antiderivative of coth (2 categories)
- Difference of cosh and sinh (2 categories)
- Tanh is odd (2 categories)
- Series for log(z) for Re(z) greater than 1/2 (2 categories)
- Digamma functional equation (2 categories)
- Taylor series of cosine (2 categories)
- Sinh of a sum (2 categories)
- E(1,1)(z)=exp(z) (2 categories)
- Asymptotic formula for partition function (2 categories)
- Sqrt(1-z^2)2F1(1,1;3/2;z^2)=arcsin(z)/z (2 categories)
- E^x is greater than 1+x for nonzero real x (2 categories)
- Value of Ai'(0) (2 categories)
- Barnes G (2 categories)
- Van der Waerden function is nowhere differentiable (2 categories)
- Error function is odd (2 categories)
- Period of sinh (2 categories)
- Weierstrass factorization of cosh (2 categories)
- Bessel J in terms of Bessel-Clifford (2 categories)
- Beta as product of gamma functions (2 categories)
- Z2F1(1,1;2,-z) equals log(1+z) (2 categories)
- Binomial coefficient (n choose 0) equals 1 (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)
- F(n+m+1)=F(n+1)F(m+1)+F(n)F(m) (2 categories)
- Product representation of totient (2 categories)
- Integral of log of inverse erf from 0 to 1 (2 categories)
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (2 categories)
- Functional equation for Riemann zeta (2 categories)
- Q-derivative power rule (2 categories)
- K(m)=(pi/2)2F1(1/2,1/2;1;m) (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)
- Reciprocal Riemann zeta in terms of Mobius (2 categories)
- L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) (2 categories)
- Recurrence relation for Struve function (2) (2 categories)
- Champernowne constant is transcendental (2 categories)
- Halving identity for tangent (2) (2 categories)
- Relationship between Bessel I and Bessel J (2 categories)
- Legendre chi in terms of Lerch transcendent (2 categories)
- Haversine (2 categories)
- Relationship between Chebyshev U and Gegenbauer C (2 categories)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (2 categories)
- Relationship between Scorer Hi and Airy functions (2 categories)
- Limiting value of Fresnel C (2 categories)
- Relationship between cosh, inverse Gudermannian, and sec (2 categories)
- Log(z)=log(10)log 10(z) (2 categories)
- Relationship between coth, inverse Gudermannian, and csc (2 categories)
- Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued) (2 categories)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (2 categories)
- Relationship between incomplete beta and hypergeometric 2F1 (2 categories)
- Logarithm of 1 (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)
- Relationship between q-derivative and derivative (2 categories)
- Derivative of Li 2(-1/x) (2 categories)
- Logarithm of quotient of Jacobi theta 3 equals a sum of sines (2 categories)
- 1Phi0(a;;z) as infinite product (2 categories)
- Relationship between sinh, inverse Gudermannian, and tan (2 categories)
- Derivative of arcsec (2 categories)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (2 categories)
- Relationship between tanh and tan (2 categories)
- Derivative of cosine integral (2 categories)
- McCarthy function is continuous (2 categories)
- Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3 (2 categories)
- Derivative of sech (2 categories)
- Sum over bottom of binomial coefficient with top fixed equals 2^n (2 categories)
- Antiderivative of arccos (2 categories)
- Riemann zeta at even integers (2 categories)
- Derivative of versine (2 categories)
- T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (2 categories)
- Antiderivative of hyperbolic cosecant (2 categories)
- Differential equation for Jacobi P (2 categories)
- Tanh of a sum (2 categories)
- Apéry's constant is irrational (2 categories)
- Series for log(z) for absolute value of (z-1) less than 1 (2 categories)
- Orthogonality of Bateman F on R (2 categories)
- Taylor series of log(1+z) (2 categories)
- Thomae function is continuous at irrationals (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)
- Value of Ai(0) (2 categories)
- Barnes G at positive integer (2 categories)
- Euler's formula (2 categories)
- Period of tanh (2 categories)
- Weierstrass factorization of cosine (2 categories)
- Euler totient is multiplicative (2 categories)
- Beta in terms of gamma (2 categories)
- Exsecant (2 categories)
- Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (2 categories)
- Binomial series (2 categories)
- 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 categories)
- Pure recurrence relation for partition function (2 categories)
- Integral of monomial times Bessel J (2 categories)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (2 categories)
- Functional equation for Riemann zeta with cosine (2 categories)
- Q-difference equation for q-exponential E sub 1/q (2 categories)
- Gamma function written as infinite product (2 categories)
- Q-number of a negative (2 categories)
- Generating function for Laguerre L (2 categories)
- Ramanujan tau inequality (2 categories)
- C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x) (2 categories)
- Knopp function is continuous (2 categories)
- L n'(0)=-n (2 categories)
- Recurrence relation for partition function with sum of divisors (2 categories)
- Halving identity for tangent (3) (2 categories)
- Relationship between Bessel I sub -1/2 and cosh (2 categories)
- Closed form for partition function with sinh (2 categories)
- Legendre chi in terms of polylogarithm (2 categories)
- Relationship between Chebyshev U and hypergeometric 2F1 (2 categories)
- Hyperfactorial in terms of K-function (2 categories)
- Relationship between Sievert integral and exponential integral E (2 categories)
- Cosh is even (2 categories)
- Limiting value of Fresnel S (2 categories)
- Relationship between cosh and cos (2 categories)
- Coth of a sum (2 categories)
- Log 10(z)=log(z)/log(10) (2 categories)
- Relationship between coth and cot (2 categories)
- Darboux function is continuous (2 categories)
- Logarithm (multivalued) of product is a sum of logarithms (multivalued) (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)
- Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm (2 categories)
- Derivative is a linear operator (2 categories)
- Logarithm of a complex number (2 categories)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 (2 categories)
- Relationship between secant, Gudermannian, and cosh (2 categories)
- Derivative of Riemann zeta (2 categories)
- Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines (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)
- Relationship between sinh and hypergeometric 0F1 (2 categories)
- Derivative of arcsin (2 categories)
- Relationship between the Fransén–Robinson constant, e, pi, and logarithm (2 categories)
- Derivative of cotangent (2 categories)
- McCarthy function is nowhere differentiable (2 categories)
- Sum of odd indexed Fibonacci numbers (2 categories)
- Derivative of sine (2 categories)
- Antiderivative of arccosh (2 categories)
- Rodrigues formula for Meixner polynomial (2 categories)
- Derivative of zeta at -1 (2 categories)
- Antiderivative of inverse error function (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)
- Taylor series of log(1-z) (2 categories)
- Doubling identity for cosh (1) (2 categories)
- Thomae function is discontinuous at rationals (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)
- Square of i (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)
- Versine (2 categories)
- Weierstrass factorization of sine (2 categories)
- Bessel at -n-1/2 in terms of Bessel polynomial (2 categories)
- Exponential (2 categories)
- Pochhammer symbol with non-negative integer subscript (2 categories)
- X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 (2 categories)
- Beta in terms of power of t over power of (1+t) (2 categories)
- Z coth(z) = 2z/(e^(2z)-1) + z (2 categories)
- Binomial theorem (2 categories)
- Integral of Bessel J for Re(nu) greater than -1 (2 categories)
- Faber F1 is continuous (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)
- Q-Euler formula for E sub q (2 categories)
- Fresnel C in terms of erf (2 categories)
- Q-difference equation for q-exponential E sub q (2 categories)
- Q-number when a=n is a natural number (2 categories)
- Generating function for partition function (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)
- 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)
- Closed formula for physicist's Hermite polynomials (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)
- Cosh of a sum (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)
- 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)
- Relationship between logarithm (multivalued) and logarithm (2 categories)
- Derivative of Bessel-Clifford (2 categories)
- Logarithm of a quotient is a difference of logarithms (2 categories)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (2 categories)
- Relationship between sech, inverse Gudermannian, and cos (2 categories)
- Derivative of Struve H0 (2 categories)
- Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines (2 categories)
- 2F1(1,1;2;z)=-log(1-z)/z (2 categories)
- Relationship between sinh and sin (2 categories)
- Derivative of arcsinh (2 categories)
- Sum of Fibonacci numbers (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)
- Relationship between the Gegenbauer C polynomials and the Jacobi P polynomials (2 categories)
- Derivative of coth (2 categories)
- Sum of reciprocal Pochhammer symbols of a fixed exponent (2 categories)
- Airy zeta function at 2 (2 categories)
- Riemann function is almost nowhere differentiable (2 categories)
- Derivative of sine integral (2 categories)
- Symmetry relation of exponential integral E (2 categories)
- Antiderivative of arcsin (2 categories)
- Möbius function is multiplicative (2 categories)
- Takagi function is continuous (2 categories)
- Antiderivative of sech (2 categories)
- Digamma at 1 (2 categories)
- Taylor series for Fresnel C (2 categories)
- Series for polygamma in terms of Riemann zeta (2 categories)
- Orthogonality of Chebyshev U on (-1,1) (2 categories)
- Taylor series of sine (2 categories)
- Doubling identity for cosh (2) (2 categories)
- Three-term recurrence for Bateman F (2 categories)
- E(m)=(pi/2)2F1(-1/2,1/2;1;m) (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)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (2 categories)
- Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 (2 categories)
- E is irrational (2 categories)
- Value of derivative of trigamma at positive integer plus 1/2 (2 categories)
- Partial derivative of beta function (2 categories)
- Wallis product (2 categories)
- Euler E generating function (2 categories)
- Weierstrass factorization of sinh (2 categories)
- Bessel at n+1/2 in terms of Bessel polynomial (2 categories)
- X/(1+x) less than log(1+x) (2 categories)
- Beta in terms of sine and cosine (2 categories)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (2 categories)
- F(-n)=(-1)^(n+1)F(n) (2 categories)
- Prime number theorem, logarithmic integral (2 categories)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (2 categories)
- Bohr-Mollerup theorem (2 categories)
- Faber F1 is nowhere differentiable (2 categories)
- Pythagorean identity for sin and cos (2 categories)
- Integral representation of Airy Ai (2 categories)
