DLMF:13.20.E11 (Q4600): Difference between revisions

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Revision as of 16:15, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 16:15, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
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		Property / Symbols used
			Q11320
		Property / Symbols used: Q11320 / rank
			Normal rank
		Property / Symbols used: Q11320 / qualifier
			Defining formula: ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$ \paraU@{\NVar{a}}{\NVar{z}}
		Property / Symbols used: Q11320 / qualifier
			xml-id: C12.S2.SS1.p1.m1adec
		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.m1hdec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Phi(\kappa,\mu,x)}}$ \Phi(\kappa,\mu,x)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C13.S20.XMD4.m1adec

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Latest revision as of 16:15, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.20.E11	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\left(\tfrac{1}{2}\mu\right)^{-\frac{1}{4}}\*\left(\frac{\kappa+\mu}{e}\right)^{\frac{1}{2}(\kappa+\mu)}\*\Phi(\kappa,\mu,x)\*U\left(\mu-\kappa,\zeta\sqrt{2\mu}\right)\left(1+O\left(\mu^{-1}\ln\mu\right)\right),}}$

0 references

DLMF id

DLMF:13.20.E11

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2addec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E3.m2abdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2abdec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2abdec

0 references

Q11320

Defining formula

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

xml-id

C12.S2.SS1.p1.m1adec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1hdec

0 references

function (locally)

Defining formula

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

xml-id

C13.S20.XMD4.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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