DLMF:14.19.E8 (Q4921): Difference between revisions

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Revision as of 13:31, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:31, 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 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.m2aedec
		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.m1cdec
		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.m1ddec
		Property / Symbols used
			Q11629
		Property / Symbols used: Q11629 / rank
			Normal rank
		Property / Symbols used: Q11629 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\xi>0}}$ \xi>0
		Property / Symbols used: Q11629 / qualifier
			xml-id: C14.S19.XMD10.m1adec

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Latest revision as of 13:31, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.19.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n-\frac{1}{2}}\left(\cosh\xi\right)=\frac{\Gamma\left(m-n+\tfrac{1}{2}\right)}{\Gamma\left(m+n+\tfrac{1}{2}\right)}\*\left(\frac{\pi}{2\sinh\xi}\right)^{1/2}P^{n}_{m-\frac{1}{2}}\left(\coth\xi\right).}}$

0 references

DLMF id

DLMF:14.19.E8

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aedec

0 references

Q11481

Defining formula

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

xml-id

C14.S21.SS1.p1.m1acdec

0 references

Q11592

Defining formula

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

xml-id

C14.S21.SS1.p1.m3addec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aedec

0 references

hyperbolic cosine function

Defining formula

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

xml-id

C4.S28.E2.m2agdec

0 references

hyperbolic cotangent function

Defining formula

${\displaystyle{\displaystyle\coth\NVar{z}}}$

xml-id

C4.S28.E7.m2aadec

0 references

hyperbolic sine function

Defining formula

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

xml-id

C4.S28.E1.m2aedec

0 references

Q11593

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C14.S1.XMD5.m1cdec

0 references

Q11602

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C14.S1.XMD6.m1ddec

0 references

Q11629

Defining formula

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

xml-id

C14.S19.XMD10.m1adec

0 references

 

Sitelinks

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