DLMF:14.25.E1 (Q4958): Difference between revisions

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Revision as of 13:41, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:41, 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
			hyperbolic cosine function
		Property / Symbols used: hyperbolic cosine function / rank
			Normal rank
		Property / Symbols used: hyperbolic cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ \cosh@@{\NVar{z}}
		Property / Symbols used: hyperbolic cosine function / qualifier
			xml-id: C4.S28.E2.m2adec
		Property / Symbols used
			hyperbolic sine function
		Property / Symbols used: hyperbolic sine function / rank
			Normal rank
		Property / Symbols used: hyperbolic sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sinh\NVar{z}}}$ \sinh@@{\NVar{z}}
		Property / Symbols used: hyperbolic sine function / qualifier
			xml-id: C4.S28.E1.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.m1adec
		Property / Symbols used
			Q11638
		Property / Symbols used: Q11638 / rank
			Normal rank
		Property / Symbols used: Q11638 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11638 / qualifier
			xml-id: C14.S1.XMD4.m1dec
		Property / Symbols used
			Q11591
		Property / Symbols used: Q11591 / rank
			Normal rank
		Property / Symbols used: Q11591 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11591 / qualifier
			xml-id: C14.S1.XMD7.m1dec
		Property / Symbols used
			Q11590
		Property / Symbols used: Q11590 / rank
			Normal rank
		Property / Symbols used: Q11590 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11590 / qualifier
			xml-id: C14.S1.XMD8.m1dec

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Latest revision as of 13:41, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.25.E1	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(z\right)=\frac{\left(z^{2}-1\right)^{\mu/2}}{2^{\nu}\Gamma\left(\mu-\nu\right)\Gamma\left(\nu+1\right)}\int_{0}^{\infty}\frac{(\sinh t)^{2\nu+1}}{(z+\cosh t)^{\nu+\mu+1}}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:14.25.E1

0 references

constraint

${\displaystyle{\displaystyle\Re\mu>\Re\nu>-1}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Q11481

Defining formula

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

xml-id

C14.S21.SS1.p1.m1adec

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.m2adec

0 references

hyperbolic sine function

Defining formula

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

xml-id

C4.S28.E1.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.m1adec

0 references

Q11638

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C14.S1.XMD4.m1dec

0 references

Q11591

Defining formula

${\displaystyle{\displaystyle\mu}}$

xml-id

C14.S1.XMD7.m1dec

0 references

Q11590

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C14.S1.XMD8.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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