DLMF:18.17.E41 (Q5782): Difference between revisions

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		Property / Symbols used
			Q11726
		Property / Symbols used: Q11726 / rank
			Normal rank
		Property / Symbols used: Q11726 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11726 / qualifier
			xml-id: C18.S1.XMD6.m1andec
		Property / Symbols used
			Q11727
		Property / Symbols used: Q11727 / rank
			Normal rank
		Property / Symbols used: Q11727 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11727 / qualifier
			xml-id: C18.S2.XMD3.m1aldec

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Latest revision as of 01:19, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.17.E41	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}\mathit{He}_{n}\left(x\right)x^{z-1}\mathrm{d}x=\Gamma\left(z+n\right)a^{-n-2}{{}_{2}F_{2}}\left({-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}\atop-\tfrac{1}{2}z-\tfrac{1}{2}n,-\tfrac{1}{2}z-\tfrac{1}{2}n+\tfrac{1}{2}};-\tfrac{1}{2}a^{2}\right),}}$

0 references

DLMF id

DLMF:18.17.E41

0 references

constraint

${\displaystyle{\displaystyle\Re a>0}}$

0 references

${\displaystyle{\displaystyle\Re z>0}}$

0 references

${\displaystyle{\displaystyle\Re z>-1}}$

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${\displaystyle{\displaystyle\Re z>0}}$

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${\displaystyle{\displaystyle n}}$

0 references

${\displaystyle{\displaystyle\Re z>-1}}$

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Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aqdec

0 references

Q11125

Defining formula

${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$

xml-id

C16.S2.m1adec

0 references

Q11525

Defining formula

${\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r14.m2ahdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aandec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2atdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aandec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1afdec

0 references

Q11750

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C18.S1.XMD2.m1hdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1andec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1aldec

0 references

 

Sitelinks

Wikipedia(0 entries)

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