DLMF:33.2.E7 (Q9502): Difference between revisions

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Revision as of 14:20, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:21, 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
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2abdec
		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.m2acdec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2acdec
		Property / Symbols used
			Q12666
		Property / Symbols used: Q12666 / rank
			Normal rank
		Property / Symbols used: Q12666 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ell}}$ \ell
		Property / Symbols used: Q12666 / qualifier
			xml-id: C33.S1.XMD2.m1fdec
		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.m1cdec
		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.m1fdec

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Latest revision as of 14:21, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:33.2.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{H^{\pm}_{\ell}}\left(\eta,\rho\right)=(\mp\mathrm{i})^{\ell}e^{(\pi\eta/2)\pm\mathrm{i}{\sigma_{\ell}}\left(\eta\right)}W_{\mp\mathrm{i}\eta,\ell+\frac{1}{2}}\left(\mp 2\mathrm{i}\rho\right),}}$

0 references

DLMF id

DLMF:33.2.E7

0 references

Symbols defined

irregular Coulomb radial functions

0 references

Symbols used

Coulomb phase shift

Defining formula

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

xml-id

C33.S2.E10.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

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2abdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2acdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2acdec

0 references

Q12666

Defining formula

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

xml-id

C33.S1.XMD2.m1fdec

0 references

Q12667

Defining formula

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

xml-id

C33.S1.XMD5.m1cdec

0 references

Q12668

Defining formula

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

xml-id

C33.S1.XMD7.m1fdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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