DLMF:14.19.E4 (Q4917): Difference between revisions

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Revision as of 13:29, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:30, 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
			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
			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
			Q11593
		Property / Symbols used: Q11593 / rank
			Normal rank
		Property / Symbols used: Q11593 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11593 / qualifier
			xml-id: C14.S1.XMD5.m1dec
		Property / Symbols used
			Q11602
		Property / Symbols used: Q11602 / rank
			Normal rank
		Property / Symbols used: Q11602 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11602 / qualifier
			xml-id: C14.S1.XMD6.m1dec
		Property / Symbols used
			Q11627
		Property / Symbols used: Q11627 / rank
			Normal rank
		Property / Symbols used: Q11627 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\xi>0}}$ \xi>0
		Property / Symbols used: Q11627 / qualifier
			xml-id: C14.S19.XMD8.m1dec

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Latest revision as of 13:30, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.19.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle P^{m}_{n-\frac{1}{2}}\left(\cosh\xi\right)=\frac{\Gamma\left(n+m+\frac{1}{2}\right)(\sinh\xi)^{m}}{2^{m}\pi^{1/2}\Gamma\left(n-m+\frac{1}{2}\right)\Gamma\left(m+\frac{1}{2}\right)}\*\int_{0}^{\pi}\frac{(\sin\phi)^{2m}}{(\cosh\xi+\cos\phi\sinh\xi)^{n+m+(1/2)}}\mathrm{d}\phi,}}$

0 references

DLMF id

DLMF:14.19.E4

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

Q11481

Defining formula

${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C14.S21.SS1.p1.m1aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2abdec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

hyperbolic cosine function

Defining formula

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

xml-id

C4.S28.E2.m2acdec

0 references

hyperbolic sine function

Defining formula

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

xml-id

C4.S28.E1.m2aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2aadec

0 references

Q11593

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C14.S1.XMD5.m1dec

0 references

Q11602

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C14.S1.XMD6.m1dec

0 references

Q11627

Defining formula

${\displaystyle{\displaystyle\xi>0}}$

xml-id

C14.S19.XMD8.m1dec

0 references

 

Sitelinks

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DRMF related sites(0 entries)

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