DLMF:10.22.E54 (Q3428): Difference between revisions

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Revision as of 17:20, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:23, 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
			Bessel function of the first kind
		Property / Symbols used: Bessel function of the first kind / rank
			Normal rank
		Property / Symbols used: Bessel function of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \BesselJ{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Bessel function of the first kind / qualifier
			xml-id: C10.S2.E2.m2aandec
		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.m2apdec
		Property / Symbols used
			Olver’s confluent hypergeometric function
		Property / Symbols used: Olver’s confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: Olver’s confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$ \OlverconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
		Property / Symbols used: Olver’s confluent hypergeometric function / qualifier
			xml-id: C13.S2.E3.m2adec
		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.m1abadec
		Property / Symbols used
			exponential function
		Property / Symbols used: exponential function / rank
			Normal rank
		Property / Symbols used: exponential function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\exp\NVar{z}}}$ \exp@@{\NVar{z}}
		Property / Symbols used: exponential function / qualifier
			xml-id: C4.S2.E19.m2acdec
		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.m3abadec
		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.m1aaidec
		Property / Symbols used
			Q11427
		Property / Symbols used: Q11427 / rank
			Normal rank
		Property / Symbols used: Q11427 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11427 / qualifier
			xml-id: C10.S1.XMD7.m1amdec

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Latest revision as of 13:23, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.22.E54	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}J_{\nu}\left(bt\right)\exp\left(-p^{2}t^{2}\right)t^{\mu-1}\mathrm{d}t=\frac{(\tfrac{1}{2}b/p)^{\nu}\Gamma\left(\tfrac{1}{2}\nu+\tfrac{1}{2}\mu\right)}{2p^{\mu}}\exp\left(-\frac{b^{2}}{4p^{2}}\right)\*{\mathbf{M}}\left(\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+1,\nu+1,\frac{b^{2}}{4p^{2}}\right),}}$

0 references

DLMF id

DLMF:10.22.E54

0 references

constraint

${\displaystyle{\displaystyle\Re(\mu+\nu)>0}}$

0 references

${\displaystyle{\displaystyle\Re(p^{2})>0}}$

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.m2aandec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2apdec

0 references

Olver’s confluent hypergeometric function

Defining formula

${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$

xml-id

C13.S2.E3.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abadec

0 references

exponential function

Defining formula

${\displaystyle{\displaystyle\exp\NVar{z}}}$

xml-id

C4.S2.E19.m2acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abadec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aaidec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1amdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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