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15
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Generalized hypergeometric function at unity

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#gamma-function #hypergeometric-function #polygamma
193
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Upper bound for the nth derivative of $\Gamma(x)^n$

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#inequality #gamma-function #upper-lower-bounds #integral-inequality #polygamma
98
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Derivatives of Polygamma Functions

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#multivariable-calculus #special-functions #digamma-function #polygamma
59
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What is the root of $\sum _{i=1}^{m-1} i^k=m^k$ given integer k?

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#number-theory #diophantine-equations #riemann-zeta #mathematica #polygamma
244
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Is there a decomposition for the digamma function as a sum of digamma functions?

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#special-functions #gamma-function #digamma-function #polygamma
93
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Polygamma function approximation to infinity

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#sequences-and-series #limits #polygamma
83
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Partial sum of polygamma

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#sequences-and-series #polygamma
211
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Another bizarre sum involving a binomial coefficient and inverse powers of integers.

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#summation #harmonic-numbers #beta-function #polygamma
191
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A convergent series for the Trigamma function $\psi_1(n) =\sum_{k=n}^{\infty} \frac1{k^2} $

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#convergence-divergence #summation #digamma-function #polygamma
120
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Simplify this expression $e^{\psi\left(\frac12+\frac{i}{2\sqrt{3}}\right)+\psi\left(\frac12-\frac{i}{2\sqrt{3}}\right)}$?

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#complex-numbers #digamma-function #polygamma
50
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a limit containing a digamma function

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#limits #digamma-function #polygamma
54
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Is there a general summation formula for the polygamma function at $z=1/2$? i.e $\psi^{(s)}(\frac{1}{2})$ for all s.

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#polygamma
377
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Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$

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#integration #sequences-and-series #digamma-function #polygamma
142
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A curious summation.

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#complex-analysis #analysis #residue-calculus #polygamma
60
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closed form in terms of a polygamma function? $ f(2,2)=\sum \sum \exp\big(- n^2k^2 \big)? $

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#sequences-and-series #closed-form #theta-functions #polygamma

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