DLMF:13.21.E13 (Q4621): Difference between revisions

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Revision as of 14:18, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 14:19, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
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		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.m2aedec
		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
			Q11090
		Property / Symbols used: Q11090 / rank
			Normal rank
		Property / Symbols used: Q11090 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar{x}\right)}}$ \envBesselJ{\NVar{\nu}}@{\NVar{x}}
		Property / Symbols used: Q11090 / qualifier
			xml-id: C2.S8.SS4.p5.m2aadec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2addec
		Property / Symbols used
			Q11566
		Property / Symbols used: Q11566 / rank
			Normal rank
		Property / Symbols used: Q11566 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11566 / qualifier
			xml-id: C13.S1.XMD4.m1kdec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}$ \Psi(\kappa,\mu,x)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C13.S21.XMD3.m1adec

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Latest revision as of 14:19, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.21.E13	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\Gamma\left(2\mu+1\right)\*\left(\frac{e^{2}}{\kappa^{2}-\mu^{2}}\right)^{\frac{1}{2}\mu}\*\left(\frac{\kappa-\mu}{\kappa+\mu}\right)^{\frac{1}{2}\kappa}\*\Psi(\kappa,\mu,x)\*\left(J_{2\mu}\left(\sqrt{\zeta\kappa}\right)+\mathrm{env}\mskip-2.0mu J_{2\mu}\left(\sqrt{\zeta\kappa}\right)O\left(\kappa^{-1}\right)\right),}}$

0 references

DLMF id

DLMF:13.21.E13

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2abdec

0 references

order not exceeding

Defining formula

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

xml-id

C2.S1.E3.m2afdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aedec

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

Q11090

Defining formula

${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS4.p5.m2aadec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2addec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1kdec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}$

xml-id

C13.S21.XMD3.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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