DLMF:25.11.E31 (Q7705)

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Language	Label	Description	Also known as
English	DLMF:25.11.E31	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}% \frac{x^{s-1}e^{-ax}}{2\cosh x}\mathrm{d}x=4^{-s}\left(\zeta\left(s,\tfrac{1}{% 4}+\tfrac{1}{4}a\right)-\zeta\left(s,\tfrac{3}{4}+\tfrac{1}{4}a\right)\right),}}

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DLMF:25.11.E31

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{\displaystyle{\displaystyle\Re s>0}}

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{\displaystyle{\displaystyle\Re a>-1}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2ahdec

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Hurwitz zeta function

Defining formula

{\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

C25.S11.E1.m2aafdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1akdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2aedec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3akdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aodec

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Sitelinks

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