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Category:Theorem
From specialfunctionswiki
Pages in category "Theorem"
The following 156 pages are in this category, out of 557 total.
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- Relationship between Chebyshev T and hypergeometric 2F1
- Relationship between Chebyshev U and Gegenbauer C
- Relationship between Chebyshev U and hypergeometric 2F1
- Relationship between cos and cosh
- Relationship between cosh and cos
- Relationship between cosh and hypergeometric 0F1
- Relationship between cosh, inverse Gudermannian, and sec
- Relationship between cosine and hypergeometric 0F1
- Relationship between cosine, Gudermannian, and sech
- Relationship between cosine, imaginary number, logarithm, and the golden ratio
- Relationship between cot and coth
- Relationship between cot, Gudermannian, and csch
- Relationship between coth and cot
- Relationship between coth and csch
- Relationship between coth, inverse Gudermannian, and csc
- Relationship between csc, Gudermannian, and coth
- Relationship between csch and csc
- Relationship between csch, inverse Gudermannian, and cot
- Relationship between dilogarithm and log(1-z)/z
- Relationship between exponential integral Ei, cosine integral, and sine integral
- Relationship between Hurwitz zeta and gamma function
- Relationship between incomplete beta and hypergeometric 2F1
- Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm
- Relationship between Lerch transcendent and Lerch zeta
- Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)
- Relationship between Li 2(1),Li 2(-1), and pi
- Relationship between logarithm (multivalued) and logarithm
- Relationship between logarithm (multivalued) and positive integer exponents
- Relationship between logarithm and Mangoldt
- Relationship between logarithm and positive integer exponents
- Relationship between logarithmic integral and exponential integral
- Relationship between Meixner polynomials and Charlier polynomials
- Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta
- Relationship between q-derivative and derivative
- Relationship between Scorer Gi and Airy functions
- Relationship between Scorer Hi and Airy functions
- Relationship between secant, Gudermannian, and cosh
- Relationship between sech and sec
- Relationship between sech, inverse Gudermannian, and cos
- Relationship between Sievert integral and exponential integral E
- Relationship between sin and sinh
- Relationship between sine and hypergeometric 0F1
- Relationship between sine, Gudermannian, and tanh
- Relationship between sine, imaginary number, logarithm, and the golden ratio
- Relationship between sinh and hypergeometric 0F1
- Relationship between sinh and sin
- Relationship between sinh, inverse Gudermannian, and tan
- Relationship between spherical Bessel j and sine
- Relationship between spherical Bessel y and cosine
- Relationship between Struve function and hypergeometric pFq
- Relationship between tan and tanh
- Relationship between tangent, Gudermannian, and sinh
- Relationship between tanh and tan
- Relationship between tanh, inverse Gudermannian, and sin
- Relationship between the exponential integral and upper incomplete gamma function
- Relationship between the Fransén–Robinson constant, e, pi, and logarithm
- Relationship between the Gegenbauer C polynomials and the Jacobi P polynomials
- Relationship between Weber function 0 and Struve function 0
- Relationship between Weber function 1 and Struve function 1
- Riemann function is almost nowhere differentiable
- Riemann function is continuous
- Riemann zeta as contour integral
- Riemann zeta as integral of monomial divided by an exponential
- Riemann zeta at even integers
- Riemann-Landau xi is even
- Rodrigues formula for Meixner polynomial
S
- Schwarz function is continuous
- Schwarz function is nowhere differentiable on a dense subset
- Series for erf with exponential factored out
- Series for log(Riemann zeta) in terms of Mangoldt function
- Series for log(riemann zeta) over primes
- Series for log(z) for absolute value of (z-1) less than 1
- Series for log(z) for Re(z) greater than 0
- Series for log(z) for Re(z) greater than 1/2
- Series for log(z+a) for positive a and Re(z) greater than -a
- Series for polygamma in terms of Riemann zeta
- Series for q-sin sub q
- Sinh is odd
- Sinh of a sum
- Sqrt(1-z^2)2F1(1,1;3/2;z^2)=arcsin(z)/z
- Square of i
- Squares of theta relation for Jacobi theta 1 and Jacobi theta 4
- Squares of theta relation for Jacobi theta 2 and Jacobi theta 4
- Squares of theta relation for Jacobi theta 3 and Jacobi theta 4
- Squares of theta relation for Jacobi theta 4 and Jacobi theta 4
- Sum of cosh and sinh
- Sum of divisors functions written in terms of partition function
- Sum of even indexed Fibonacci numbers
- Sum of Fibonacci numbers
- Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3
- Sum of Lucas numbers
- Sum of odd indexed Fibonacci numbers
- Sum of reciprocal Pochhammer symbols of a fixed exponent
- Sum of squares of Fibonacci numbers
- Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1
- Sum of totient equals z/((1-z) squared)
- Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2
- Sum of values of sinc
- Sum over bottom of binomial coefficient with top fixed equals 2^n
- Symmetry relation of exponential integral E
T
- T (n+1)(x)-2xT n(x)+T (n-1)(x)=0
- T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n
- T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k)
- T(n)^2=T(T(n))+T(T(n)-1)
- T(n+1)=T(n)+n+1
- T(n+1)^2-T(n)^2=(n+1)^3
- Takagi function is continuous
- Takagi function is nowhere differentiable
- Tanh is odd
- Tanh of a sum
- Taylor series for error function
- Taylor series for Fresnel C
- Taylor series for Fresnel S
- Taylor series for Gudermannian
- Taylor series for sinh
- Taylor series of cosine
- Taylor series of log(1+z)
- Taylor series of log(1-z)
- Taylor series of sine
- Taylor series of the exponential function
- The Euler-Mascheroni constant exists
- The Petr function is continuous
- The Petr function is nowhere differentiable
- Thomae function is continuous at irrationals
- Thomae function is discontinuous at rationals
- Three-term recurrence for Bateman F
- Two-sided inequality for e^(x^2) integral from x to infinity e^(-t^2) dt for non-negative real x
U
V
W
- Wallis product
- Weierstrass elementary factors inequality
- Weierstrass factorization of cosh
- Weierstrass factorization of cosine
- Weierstrass factorization of sine
- Weierstrass factorization of sinh
- Weierstrass factorization theorem
- Weierstrass function is continuous
- Weierstrass function is nowhere differentiable