DLMF:23.11.E3 (Q7322): Difference between revisions

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Revision as of 16:01, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 16:01, 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
			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.m2aadec
		Property / Symbols used
			Q12055
		Property / Symbols used: Q12055 / rank
			Normal rank
		Property / Symbols used: Q12055 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbb{L}}}$ \mathbb{L}
		Property / Symbols used: Q12055 / qualifier
			xml-id: C23.S1.XMD1.m1adec
		Property / Symbols used
			Q12056
		Property / Symbols used: Q12056 / rank
			Normal rank
		Property / Symbols used: Q12056 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q12056 / qualifier
			xml-id: C23.S1.XMD7.m1adec
		Property / Symbols used
			Q12068
		Property / Symbols used: Q12068 / rank
			Normal rank
		Property / Symbols used: Q12068 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tau}}$ \tau
		Property / Symbols used: Q12068 / qualifier
			xml-id: C23.S1.XMD9.m1bdec
		Property / Symbols used
			Q12082
		Property / Symbols used: Q12082 / rank
			Normal rank
		Property / Symbols used: Q12082 / qualifier
			Defining formula: ${\displaystyle{\displaystyle f_{j}(s,\tau)}}$ f_{j}(s,\tau)
		Property / Symbols used: Q12082 / qualifier
			xml-id: C23.S11.XMD1.m1bdec

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Latest revision as of 16:01, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:23.11.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\zeta\left(z\right)=\frac{1}{z}+\int_{0}^{\infty}\left(e^{-s}\left(zs-\sinh\left(zs\right)\right)f_{1}(s,\tau)-e^{i\tau s}\left(zs-\sin\left(zs\right)\right)f_{2}(s,\tau)\right)\mathrm{d}s,}}$

0 references

DLMF id

DLMF:23.11.E3

0 references

Symbols used

DLMF:23.2.E5

Defining formula

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

xml-id

C23.S2.E5.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aadec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2abdec

0 references

hyperbolic sine function

Defining formula

${\displaystyle{\displaystyle\sinh\NVar{z}}}$

xml-id

C4.S28.E1.m2aadec

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.m3aadec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2aadec

0 references

Q12055

Defining formula

${\displaystyle{\displaystyle\mathbb{L}}}$

xml-id

C23.S1.XMD1.m1adec

0 references

Q12056

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C23.S1.XMD7.m1adec

0 references

Q12068

Defining formula

${\displaystyle{\displaystyle\tau}}$

xml-id

C23.S1.XMD9.m1bdec

0 references

Q12082

Defining formula

${\displaystyle{\displaystyle f_{j}(s,\tau)}}$

xml-id

C23.S11.XMD1.m1bdec

0 references

 

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