DLMF:13.21.E14 (Q4622): Difference between revisions

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Revision as of 16:19, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 16:19, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
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		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.m2aedec
		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
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aadec
		Property / Symbols used
			Q11566
		Property / Symbols used: Q11566 / rank
			Normal rank
		Property / Symbols used: Q11566 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11566 / qualifier
			xml-id: C13.S1.XMD4.m1ldec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle c(\kappa,\mu)}}$ c(\kappa,\mu)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C13.S21.XMD1.m1adec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}$ \Psi(\kappa,\mu,x)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C13.S21.XMD3.m1bdec

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Latest revision as of 16:19, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.21.E14	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\frac{e^{-\mu\pi\mathrm{i}}}{\pi}\Gamma\left(\kappa+\mu+\tfrac{1}{2}\right)\*\Gamma\left(\kappa-\mu+\tfrac{1}{2}\right)\*c(\kappa,\mu)\Psi(\kappa,\mu,x)\*\left(\sin\left(\kappa\pi-\mu\pi\right)J_{2\mu}\left(\sqrt{\zeta\kappa}\right)-\cos\left(\kappa\pi-\mu\pi\right)Y_{2\mu}\left(\sqrt{\zeta\kappa}\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(\sqrt{\zeta\kappa}\right)O\left(\kappa^{-1}\right)\right),}}$

0 references

DLMF id

DLMF:13.21.E14

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.m2acdec

0 references

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2aadec

0 references

order not exceeding

Defining formula

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

xml-id

C2.S1.E3.m2agdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2afdec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E3.m2addec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

Q11091

Defining formula

${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS4.p5.m4acdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aedec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2acdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aadec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1ldec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle c(\kappa,\mu)}}$

xml-id

C13.S21.XMD1.m1adec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}$

xml-id

C13.S21.XMD3.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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