DLMF:25.14.E5 (Q7744): Difference between revisions

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Revision as of 01:03, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:03, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		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.m1adec
		Property / Symbols used
			Q10784
		Property / Symbols used: Q10784 / rank
			Normal rank
		Property / Symbols used: Q10784 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\in}}$ \in
		Property / Symbols used: Q10784 / qualifier
			xml-id: introduction.Sx4.p1.t1.r10.m2adec
		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.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.m3adec
		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.m1acdec
		Property / Symbols used
			Q10785
		Property / Symbols used: Q10785 / rank
			Normal rank
		Property / Symbols used: Q10785 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\setminus}}$ \setminus
		Property / Symbols used: Q10785 / qualifier
			xml-id: introduction.Sx4.p2.t1.r19.m2adec
		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.m1dec
		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.m1cdec
		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.m1ddec
		Property / Symbols used
			Q12156
		Property / Symbols used: Q12156 / rank
			Normal rank
		Property / Symbols used: Q12156 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q12156 / qualifier
			xml-id: C25.S1.XMD8.m1cdec

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Latest revision as of 01:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.14.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Phi\left(z,s,a\right)=\frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}\frac{x^{s-1}e^{-ax}}{1-ze^{-x}}\mathrm{d}x,}}$

0 references

DLMF id

DLMF:25.14.E5

0 references

constraint

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

0 references

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

0 references

${\displaystyle{\displaystyle z\in\mathbb{C}\setminus[1,\infty)}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Lerch’s transcendent

Defining formula

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

xml-id

C25.S14.E1.m2addec

0 references

Q11243

Defining formula

${\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}$

xml-id

introduction.Sx4.p2.t1.r1.m4adec

0 references

Q10923

Defining formula

${\displaystyle{\displaystyle\mathbb{C}}}$

xml-id

introduction.Sx4.p1.t1.r1.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1acdec

0 references

Q10785

Defining formula

${\displaystyle{\displaystyle\setminus}}$

xml-id

introduction.Sx4.p2.t1.r19.m2adec

0 references

Q12152

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C25.S1.XMD5.m1dec

0 references

Q12161

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C25.S1.XMD6.m1cdec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1ddec

0 references

Q12156

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C25.S1.XMD8.m1cdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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