DLMF:25.11.E31 (Q7705): Difference between revisions

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Revision as of 18:17, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:43, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\Re a>-1}}$ \realpart@@{a}>-1
		Property / constraint: ${\displaystyle{\displaystyle\Re a>-1}}$ / rank
			Normal rank
		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2ahdec
		Property / Symbols used
			Hurwitz zeta function
		Property / Symbols used: Hurwitz zeta function / rank
			Normal rank
		Property / Symbols used: Hurwitz zeta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$ \Hurwitzzeta@{\NVar{s}}{\NVar{a}}
		Property / Symbols used: Hurwitz zeta function / qualifier
			xml-id: C25.S11.E1.m2aafdec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1akdec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2aedec
		Property / Symbols used
			hyperbolic cosine function
		Property / Symbols used: hyperbolic cosine function / rank
			Normal rank
		Property / Symbols used: hyperbolic cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ \cosh@@{\NVar{z}}
		Property / Symbols used: hyperbolic cosine function / qualifier
			xml-id: C4.S28.E2.m2adec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3akdec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1aodec
		Property / Symbols used
			Q12152
		Property / Symbols used: Q12152 / rank
			Normal rank
		Property / Symbols used: Q12152 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12152 / qualifier
			xml-id: C25.S1.XMD5.m1ldec
		Property / Symbols used
			Q12161
		Property / Symbols used: Q12161 / rank
			Normal rank
		Property / Symbols used: Q12161 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q12161 / qualifier
			xml-id: C25.S1.XMD6.m1zdec
		Property / Symbols used
			Q12149
		Property / Symbols used: Q12149 / rank
			Normal rank
		Property / Symbols used: Q12149 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q12149 / qualifier
			xml-id: C25.S1.XMD7.m1wdec

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Latest revision as of 13:43, 2 January 2020

No description defined

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

Statements

Defining formula

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

0 references

DLMF id

DLMF:25.11.E31

0 references

constraint

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

0 references

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

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2ahdec

0 references

Hurwitz zeta function

Defining formula

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

xml-id

C25.S11.E1.m2aafdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1akdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aedec

0 references

hyperbolic cosine function

Defining formula

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

xml-id

C4.S28.E2.m2adec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3akdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1aodec

0 references

Q12152

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C25.S1.XMD5.m1ldec

0 references

Q12161

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C25.S1.XMD6.m1zdec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1wdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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