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Relation between the derivative of hurwitz zeta and trigamma

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#integration #sequences-and-series #special-functions #riemann-zeta #polygamma
133
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Prove or disprove: Is $\psi(x) - \psi(x + y)$ an increasing function of $x > 0$, for all $y > 0$?

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#gamma-function #polygamma
75
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Does the following digamma/trigamma inequality hold? And can it be formally shown?

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#real-analysis #inequality #special-functions #gamma-function #polygamma
142
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Closed form for $\sum_{k\geq 1}\frac{1}{(2^k-1)^a}$

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#summation #special-functions #closed-form #polygamma
149
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Convexity of reciprocal polygamma

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#convex-analysis #zeta-functions #polygamma
90
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Path containing zeros of all derivatives

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#complex-analysis #gamma-function #polygamma #meromorphic-functions
962
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Solve the system of equations in the maximum likelihood estimation of Gamma distribution parameters

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#gamma-function #maximum-likelihood #gamma-distribution #polygamma #digamma-function
385
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Asymptotic behavior of Harmonic-like series $\sum_{n=1}^{k} \psi(n) \psi'(n) - (\ln k)^2/2$ as $k \to \infty$

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#sequences-and-series #asymptotics #polygamma #stieltjes-constants
1k
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Asymptotic expansion of Polygamma functions

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#real-analysis #complex-analysis #asymptotics #gamma-function #polygamma
32
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How to sum this vaguely zeta-looking function to QGammafunctions?

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#real-analysis #summation #logarithms #zeta-functions #polygamma
132
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Closed form expression for $\psi_{e^{\pi}}^{(3)}(1)$

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#complex-analysis #number-theory #mathematica #digamma-function #polygamma
144
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Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

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#complex-analysis #number-theory #mathematica #digamma-function #polygamma
328
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Closed form expression for an integral

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#complex-analysis #number-theory #mathematica #digamma-function #polygamma
164
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Integral representation of Bell Polynomial?

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#calculus #analysis #gamma-function #polygamma #bell-numbers
43
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Asymptotic behavior of $\psi^{(n)}(1/2+ix)$ as $n\to\infty$?

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#asymptotics #special-functions #approximation #zeta-functions #polygamma

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