DLMF:13.23.E3 (Q4637): Difference between revisions

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Revision as of 00:01, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:22, 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
			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.m1abdec
		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2abdec
		Property / Symbols used
			Whittaker confluent hypergeometric function
		Property / Symbols used: Whittaker confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ \WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			xml-id: C13.S14.E2.m2abdec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1abdec

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Latest revision as of 15:22, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.23.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\mu+\nu+\frac{1}{2}\right)\Gamma\left(\kappa-\nu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)\Gamma\left(\frac{1}{2}+\mu-\nu\right)},}}$

0 references

DLMF id

DLMF:13.23.E3

0 references

constraint

${\displaystyle{\displaystyle-\tfrac{1}{2}-\Re\mu<\Re\nu<\Re\kappa}}$

0 references

Symbols used

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2abdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1abdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

0 references

Whittaker confluent hypergeometric function

Defining formula

${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$

xml-id

C13.S14.E2.m2abdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abdec

0 references

 

Sitelinks

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