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- Gelfond-Schneider constant is transcendental (2 categories)
- Generating relation for Bateman F (2 categories)
- Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 (2 categories)
- Sum of cosh and sinh (2 categories)
- Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 (2 categories)
- Hankel H (1) in terms of csc and Bessel J (2 categories)
- Complex conjugate of argument of error function (2 categories)
- T(n+1)=T(n)+n+1 (2 categories)
- Hermite (physicist) polynomial at negative argument (2 categories)
- Contour integral representation of reciprocal gamma (2 categories)
- Taylor series for Gudermannian (2 categories)
- Coversine (2 categories)
- The Euler-Mascheroni constant exists (2 categories)
- (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0 (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)
- Integral representation of Struve function (3) (2 categories)
- -log(1-x) less than x/(1-x) (2 categories)
- Derivative of Bessel Y with respect to its order (2 categories)
- 1/q-number as a q-number (2 categories)
- Derivative of arccosh (2 categories)
- 2F1(1/2,1;3/2;-z^2)=arctan(z)/z (2 categories)
- Derivative of arctanh (2 categories)
- Weierstrass elementary factors inequality (2 categories)
- Abs(log(1-x)) less than 3x/2 (2 categories)
- Derivative of hyperbolic cosecant (2 categories)
- Weierstrass function is nowhere differentiable (2 categories)
- Alternating sum over bottom of binomial coefficient with top fixed equals 0 (2 categories)
- Derivative of tangent (2 categories)
- X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 (2 categories)
- Antiderivative of arctan (2 categories)
- Devil's staircase is not absolutely continuous (2 categories)
- Antiderivative of tanh (2 categories)
- Digamma at n+1 (2 categories)
- Arcsin as inverse sine (2 categories)
- Doubling identity for sinh (1) (2 categories)
- E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1 (2 categories)
- 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 categories)
- Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (2 categories)
- Bessel polynomial in terms of Bessel functions (2 categories)
- F(2n)=F(n+1)^2-F(n-1)^2 (2 categories)
- Bolzano function is continuous (2 categories)
- Faber F2 is continuous (2 categories)
- Fibonacci zeta at 1 is irrational (2 categories)
- Gamma(1)=1 (2 categories)
- Catalan's constant using Dirichlet beta (2 categories)
- Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 (2 categories)
- H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (2 categories)
- Cellérier function is continuous (2 categories)
- Sum of totient equals z/((1-z) squared) (2 categories)
- Constant functions are elliptic functions (2 categories)
- T(n+1)^2-T(n)^2=(n+1)^3 (2 categories)
- The Petr function is continuous (2 categories)
- (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0 (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)
- Integral representation of polygamma 2 (2 categories)
- Q-Gamma at 1 (2 categories)
- 0!=1 (2 categories)
- Derivative of Gudermannian (2 categories)
- 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 categories)
- Derivative of arccot (2 categories)
- Van der Waerden function is continuous (2 categories)
- 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z) (2 categories)
- Derivative of cosecant (2 categories)
- Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1 (2 categories)
- Derivative of inverse error function (2 categories)
- Derivative of tanh (2 categories)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (2 categories)
- Antiderivative of arctanh (2 categories)
- Antiderivative of the logarithm (2 categories)
- Digamma at n+1/2 (2 categories)
- Doubling identity for sinh (2) (2 categories)
- E^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0) (2 categories)
- B(x,y+1)=(y/(x+y))B(x,y) (2 categories)
- Binet's formula (2 categories)
- F(2n+1)=F(n+1)^2+F(n)^2 (2 categories)
- Bolzano function is nowhere differentiable (2 categories)
- Faber F2 is nowhere differentiable (2 categories)
- Fresnel S in terms of erf (2 categories)
- Gamma(n+1)=n! (2 categories)
- Gelfond constant is transcendental (2 categories)
- Catalan's constant using Hurwitz zeta (2 categories)
- H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (2 categories)
- Cellérier function is nowhere differentiable (2 categories)
- Sum of divisors functions written in terms of partition function (2 categories)
- Halving identity for cosh (2 categories)
- Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 (2 categories)
- Hankel H (2) in terms of csc and Bessel J (2 categories)
- Constant multiple rule for derivatives (2 categories)
- T (n+1)(x)-2xT n(x)+T (n-1)(x)=0 (2 categories)
- Copeland-Erdős is irrational (2 categories)
- Taylor series for sinh (2 categories)
- The Petr function is nowhere differentiable (2 categories)
- (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0 (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)
- Integral representation of polygamma for Re(z) greater than 0 (2 categories)
- Q-Gamma at z+1 (2 categories)
- 0F0(;;z)=exp(z) (2 categories)
- Derivative of Jacobi theta 1 at 0 (2 categories)
- Value of Ai'(0) (2 categories)
- 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) (2 categories)
- Derivative of arccoth (2 categories)
- Van der Waerden function is nowhere differentiable (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)
- Derivative of cosh (2 categories)
- Weierstrass factorization of cosh (2 categories)
- Absolute convergence of secant zeta function (2 categories)
- Z2F1(1,1;2,-z) equals log(1+z) (2 categories)
- Antiderivative of cosine integral (2 categories)
- Antiderivative of versine (2 categories)
- Digamma at z+n (2 categories)
- Dirichlet function is nowhere continuous (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)
- Euler product for Riemann zeta (2 categories)
- Beta as improper integral (2 categories)
- Exponential integral Ei series (2 categories)
- F(n+1)F(n-1)-F(n)^2=(-1)^n (2 categories)
- Fresnel S is odd (2 categories)
- Gamma(z)Gamma(1-z)=pi/sin(pi z) (2 categories)
- Catalan's constant using Legendre chi (2 categories)
- H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) (2 categories)
- Sum of even indexed Fibonacci numbers (2 categories)
- Halving identity for sinh (2 categories)
- Sum of values of sinc (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)
- Copeland-Erdős is normal (2 categories)
- Tanh is odd (2 categories)
- Taylor series of cosine (2 categories)
- D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) (2 categories)
- (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 (2 categories)
- Q-derivative power rule (2 categories)
- K(m)=(pi/2)2F1(1/2,1/2;1;m) (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)
- Relationship between Bessel I and Bessel J (2 categories)
- Legendre chi in terms of Lerch transcendent (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)
- Relationship between incomplete beta and hypergeometric 2F1 (2 categories)
- Logarithm of 1 (2 categories)
- Relationship between q-derivative and derivative (2 categories)
- Logarithm of quotient of Jacobi theta 3 equals a sum of sines (2 categories)
- Relationship between sinh, inverse Gudermannian, and tan (2 categories)
- Relationship between tanh and tan (2 categories)
- McCarthy function is continuous (2 categories)
- Riemann zeta at even integers (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)
- Period of tanh (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+bt)^(-x-y) dt = b^(-x) B(x,y) (2 categories)
- 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (2 categories)
- Derivative of Legendre chi 2 (2 categories)
- Value of Ai(0) (2 categories)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (2 categories)
- Derivative of arccsc (2 categories)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (2 categories)
- Derivative of cosine (2 categories)
- Weierstrass factorization of cosine (2 categories)
- Derivative of secant (2 categories)
- Derivative of the logarithm (2 categories)
- Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (2 categories)
- Antiderivative of coth (2 categories)
