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Category:Unproven
From specialfunctionswiki
Pages in category "Unproven"
The following 200 pages are in this category, out of 495 total.
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- Limit of x^a log(x)=0
- Limiting value of Fresnel C
- Limiting value of Fresnel S
- Log 10(z)=log 10(e)log(z)
- Log 10(z)=log(z)/log(10)
- Log a(b)=1/log b(a)
- Log base a in terms of logarithm base b
- Log e(z)=log(z)
- Log((1+z)/(1-z)) as continued fraction
- Log(1+x) less than x
- Log(1+z) as continued fraction
- Log(x) less than or equal to n(x^(1/n)-1)
- Log(x) less than or equal to x-1
- Log(z)=log(10)log 10(z)
- Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued)
- Logarithm (multivalued) of product is a sum of logarithms (multivalued)
- Logarithm at -i
- Logarithm at i
- Logarithm at minus 1
- Logarithm diverges to negative infinity at 0 from right
- Logarithm of a complex number
- Logarithm of a quotient is a difference of logarithms
- Logarithm of a quotient of Jacobi theta 4 equals a sum of sines
- Logarithm of product is a sum of logarithms
- Logarithm of quotient of Jacobi theta 1 equals the log of a quotient of sines + a sum of sines
- Logarithm of quotient of Jacobi theta 2 equals the log of a quotient of cosines + a sum of sines
- Logarithm of quotient of Jacobi theta 3 equals a sum of sines
- Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines
- Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines
- Logarithmic derivative of Jacobi theta 3 equals a sum of sines
- Logarithmic derivative of Jacobi theta 4 equals a sum of sines
- Logarithmic derivative of Riemann zeta in terms of Mangoldt function
- Logarithmic derivative of Riemann zeta in terms of series over primes
M
N
O
P
- Partial derivative of beta function
- Pell constant is irrational
- Period of cosh
- Period of sinh
- Period of tanh
- Pi is irrational
- Pochhammer symbol with non-negative integer subscript
- Polygamma multiplication formula
- Polygamma recurrence relation
- Polygamma reflection formula
- Polygamma series representation
- Prime number theorem, logarithmic integral
- Prime number theorem, pi and x/log(x)
- Product of Weierstrass elementary factors is entire
- Product representation of q-exponential E sub 1/q
- Product representation of totient
- Pure recurrence relation for partition function
- Pythagorean identity for coth and csch
- Pythagorean identity for tanh and sech
Q
- Q-derivative of q-Cosine
- Q-derivative of q-Sine
- Q-derivative power rule
- Q-difference equation for q-exponential E sub 1/q
- Q-difference equation for q-exponential E sub q
- Q-Euler formula for e sub q
- Q-Euler formula for E sub q
- Q-Gamma at 1
- Q-Gamma at z+1
- Q-number of a negative
- Q-number when a=n is a natural number
R
- Ramanujan tau inequality
- Ramanujan tau is multiplicative
- Ramanujan tau of a power of a prime
- Real and imaginary parts of log
- Reciprocal gamma is entire
- Reciprocal gamma written as an infinite product
- Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1
- Reciprocal Riemann zeta in terms of Mobius
- Recurrence relation for partition function with sum of divisors
- Recurrence relation for Struve fuction
- Recurrence relation for Struve function (2)
- Recurrence relation of exponential integral E
- Relation between polygamma and Hurwitz zeta
- Relationship between Airy Ai and modified Bessel K
- Relationship between Airy Bi and modified Bessel I
- Relationship between Anger function and Bessel J
- Relationship between arcsin and arccsc
- Relationship between Bessel I and Bessel J
- Relationship between Bessel I sub -1/2 and cosh
- Relationship between Bessel I sub 1/2 and sinh
- Relationship between Bessel J and hypergeometric 0F1
- Relationship between Bessel J sub n and Bessel J sub -n
- Relationship between Bessel Y sub n and Bessel Y sub -n
- Relationship between Bessel-Clifford and hypergeometric 0F1
- Relationship between Chebyshev T and Gegenbauer C
- Relationship between Chebyshev T and hypergeometric 2F1
- Relationship between Chebyshev U and Gegenbauer C
- Relationship between Chebyshev U and hypergeometric 2F1
- 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 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, 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
- 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