DLMF:33.2.E4 (Q9499): Difference between revisions

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		Property / Symbols used
			Q12667
		Property / Symbols used: Q12667 / rank
			Normal rank
		Property / Symbols used: Q12667 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\rho}}$ \rho
		Property / Symbols used: Q12667 / qualifier
			xml-id: C33.S1.XMD5.m1bdec
		Property / Symbols used
			Q12668
		Property / Symbols used: Q12668 / rank
			Normal rank
		Property / Symbols used: Q12668 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\eta}}$ \eta
		Property / Symbols used: Q12668 / qualifier
			xml-id: C33.S1.XMD7.m1cdec

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Latest revision as of 14:20, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:33.2.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=C_{\ell}\left(\eta\right)\rho^{\ell+1}e^{\mp\mathrm{i}\rho}M\left(\ell+1\mp\mathrm{i}\eta,2\ell+2,\pm 2\mathrm{i}\rho\right),}}$

0 references

DLMF id

DLMF:33.2.E4

0 references

Symbols used

normalizing constant for Coulomb radial functions

Defining formula

${\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}$

xml-id

C33.S2.E5.m2aadec

0 references

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

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2aadec

0 references

regular Coulomb radial function

Defining formula

${\displaystyle{\displaystyle F_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}\right)}}$

xml-id

C33.S2.E3.m2aadec

0 references

Q12666

Defining formula

${\displaystyle{\displaystyle\ell}}$

xml-id

C33.S1.XMD2.m1cdec

0 references

Q12667

Defining formula

${\displaystyle{\displaystyle\rho}}$

xml-id

C33.S1.XMD5.m1bdec

0 references

Q12668

Defining formula

${\displaystyle{\displaystyle\eta}}$

xml-id

C33.S1.XMD7.m1cdec

0 references

 

Sitelinks

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