DLMF:2.5.E47 (Q823): Difference between revisions

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Revision as of 17:08, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 17:08, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Euler’s constant
		Property / Symbols used: Euler’s constant / rank
			Normal rank
		Property / Symbols used: Euler’s constant / qualifier
			Defining formula: ${\displaystyle{\displaystyle\gamma}}$ \EulerConstant
		Property / Symbols used: Euler’s constant / qualifier
			xml-id: C5.S2.E3.m2adec
		Property / Symbols used
			Mellin transform
		Property / Symbols used: Mellin transform / rank
			Normal rank
		Property / Symbols used: Mellin transform / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$ \Mellintrans@{\NVar{f}}@{\NVar{s}}
		Property / Symbols used: Mellin transform / qualifier
			xml-id: C1.S14.E32.m2asdec
		Property / Symbols used
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2aedec
		Property / Symbols used
			Q10960
		Property / Symbols used: Q10960 / rank
			Normal rank
		Property / Symbols used: Q10960 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Residue}}$ \Residue
		Property / Symbols used: Q10960 / qualifier
			xml-id: C1.S10.SS3.p5.m4afdec
		Property / Symbols used
			Q11005
		Property / Symbols used: Q11005 / rank
			Normal rank
		Property / Symbols used: Q11005 / qualifier
			Defining formula: ${\displaystyle{\displaystyle h(x)}}$ h(x)
		Property / Symbols used: Q11005 / qualifier
			xml-id: C2.S5.XMD16.m1rdec

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Latest revision as of 17:08, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:2.5.E47	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Residue_{z=1}\left[-\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]=\left(-\ln\zeta-\gamma\right)-\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(1\right),}}$

0 references

DLMF id

DLMF:2.5.E47

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aidec

0 references

Euler’s constant

Defining formula

${\displaystyle{\displaystyle\gamma}}$

xml-id

C5.S2.E3.m2adec

0 references

Mellin transform

Defining formula

${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$

xml-id

C1.S14.E32.m2asdec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2aedec

0 references

Q10960

Defining formula

${\displaystyle{\displaystyle\Residue}}$

xml-id

C1.S10.SS3.p5.m4afdec

0 references

Q11005

Defining formula

${\displaystyle{\displaystyle h(x)}}$

xml-id

C2.S5.XMD16.m1rdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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