DLMF:5.9.E17 (Q2106): Difference between revisions

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Revision as of 19:38, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 19:39, 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
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2abdec
		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.m3apdec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2acdec
		Property / Symbols used
			Q11282
		Property / Symbols used: Q11282 / rank
			Normal rank
		Property / Symbols used: Q11282 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q11282 / qualifier
			xml-id: C5.S1.XMD11.m1adec
		Property / Symbols used
			Q11273
		Property / Symbols used: Q11273 / rank
			Normal rank
		Property / Symbols used: Q11273 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11273 / qualifier
			xml-id: C5.S1.XMD7.m1ndec

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Latest revision as of 19:39, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.9.E17	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\psi\left(z+1\right)=-\gamma+\frac{1}{2\pi i}\int_{-c-\infty i}^{-c+\infty i}\frac{\pi z^{-s-1}}{\sin\left(\pi s\right)}\zeta\left(-s\right)\mathrm{d}s,}}$

0 references

DLMF id

DLMF:5.9.E17

0 references

Symbols used

Euler’s constant

Defining formula

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

xml-id

C5.S2.E3.m2abdec

0 references

Riemann zeta function

Defining formula

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

xml-id

C25.S2.E1.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2ahdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1apdec

0 references

psi (or digamma) function

Defining formula

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

xml-id

C5.S2.E2.m2aedec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2abdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3apdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2acdec

0 references

Q11282

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C5.S1.XMD11.m1adec

0 references

Q11273

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C5.S1.XMD7.m1ndec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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