DLMF:14.18.E4 (Q4905): Difference between revisions

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Revision as of 13:27, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:27, 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
			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.m1bdec
		Property / Symbols used
			Q11624
		Property / Symbols used: Q11624 / rank
			Normal rank
		Property / Symbols used: Q11624 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\phi}}$ \phi
		Property / Symbols used: Q11624 / qualifier
			xml-id: C14.S18.XMD2.m1cdec
		Property / Symbols used
			Q11625
		Property / Symbols used: Q11625 / rank
			Normal rank
		Property / Symbols used: Q11625 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\xi_{1}}}$ \xi_{1}
		Property / Symbols used: Q11625 / qualifier
			xml-id: C14.S18.XMD3.m1dec

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Latest revision as of 13:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.18.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle P_{\nu}\left(\cosh\xi_{1}\cosh\xi_{2}-\sinh\xi_{1}\sinh\xi_{2}\cos\phi\right)=P_{\nu}\left(\cosh\xi_{1}\right)P_{\nu}\left(\cosh\xi_{2}\right)+2\sum_{m=1}^{\infty}(-1)^{m}P^{-m}_{\nu}\left(\cosh\xi_{1}\right)P^{m}_{\nu}\left(\cosh\xi_{2}\right)\cos\left(m\phi\right),}}$

0 references

DLMF id

DLMF:14.18.E4

0 references

Symbols used

Q11481

Defining formula

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

xml-id

C14.S21.SS1.p1.m1adec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2acdec

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

Q11447

Defining formula

${\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}\left(z\right)}}$

xml-id

C14.S2.SS2.p2.m3adec

0 references

Q11593

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C14.S1.XMD5.m1cdec

0 references

Q11590

Defining formula

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

xml-id

C14.S1.XMD8.m1bdec

0 references

Q11624

Defining formula

${\displaystyle{\displaystyle\phi}}$

xml-id

C14.S18.XMD2.m1cdec

0 references

Q11625

Defining formula

${\displaystyle{\displaystyle\xi_{1}}}$

xml-id

C14.S18.XMD3.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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