DLMF:18.11.E2 (Q5636): Difference between revisions

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		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.m2adec
		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: ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ \WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			xml-id: C13.S14.E3.m2adec
		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.m2adec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5adec
		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.m1adec
		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.m1adec

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Latest revision as of 15:29, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.11.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x\right)=\frac{{\left(\alpha+1\right)_{n}}}{n!}M\left(-n,\alpha+1,x\right)=\frac{(-1)^{n}}{n!}U\left(-n,\alpha+1,x\right)=\frac{{\left(\alpha+1\right)_{n}}}{n!}x^{-\frac{1}{2}(\alpha+1)}e^{\frac{1}{2}x}M_{n+\frac{1}{2}(\alpha+1),\frac{1}{2}\alpha}\left(x\right)=\frac{(-1)^{n}}{n!}x^{-\frac{1}{2}(\alpha+1)}e^{\frac{1}{2}x}W_{n+\frac{1}{2}(\alpha+1),\frac{1}{2}\alpha}\left(x\right).}}$

0 references

DLMF id

DLMF:18.11.E2

0 references

Symbols used

$$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function

Defining formula

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

xml-id

C13.S2.E2.m2adec

0 references

Kummer confluent hypergeometric function

Defining formula

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

xml-id

C13.S2.E6.m2adec

0 references

Q11333

Defining formula

${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r12.m2adec

0 references

Q10759

Defining formula

${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$

xml-id

C5.S2.SS3.m1aadec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E2.m2adec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E3.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5adec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1adec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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