DLMF:13.8.E8 (Q4433): Difference between revisions

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Revision as of 15:57, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:57, 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
			Kummer confluent hypergeometric function
		Property / Symbols used: Kummer confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: Kummer confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$ \KummerconfhyperU@{\NVar{a}}{\NVar{b}}{\NVar{z}}
		Property / Symbols used: Kummer confluent hypergeometric function / qualifier
			xml-id: C13.S2.E6.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
			hyperbolic tangent function
		Property / Symbols used: hyperbolic tangent function / rank
			Normal rank
		Property / Symbols used: hyperbolic tangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tanh\NVar{z}}}$ \tanh@@{\NVar{z}}
		Property / Symbols used: hyperbolic tangent function / qualifier
			xml-id: C4.S28.E4.m2adec
		Property / Symbols used
			modified Bessel function of the second kind
		Property / Symbols used: modified Bessel function of the second kind / rank
			Normal rank
		Property / Symbols used: modified Bessel function of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \modBesselK{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: modified Bessel function of the second kind / qualifier
			xml-id: C10.S25.E3.m2adec
		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.m1dec

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Latest revision as of 15:57, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.8.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle U\left(a,b,x\right)=\frac{2e^{\frac{1}{2}x}}{\Gamma\left(a\right)}\left(\sqrt{\frac{2}{\beta}\tanh\left(\frac{w}{2}\right)}\left(\frac{1-e^{-w}}{\beta}\right)^{-b}\beta^{1-b}K_{1-b}\left(2\beta a\right)+a^{-1}\left(\frac{a^{-1}+\beta}{1+\beta}\right)^{1-b}e^{-2\beta a}O\left(1\right)\right),}}$

0 references

DLMF id

DLMF:13.8.E8

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2acdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2acdec

0 references

Kummer confluent hypergeometric function

Defining formula

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

xml-id

C13.S2.E6.m2abdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2acdec

0 references

hyperbolic tangent function

Defining formula

${\displaystyle{\displaystyle\tanh\NVar{z}}}$

xml-id

C4.S28.E4.m2adec

0 references

modified Bessel function of the second kind

Defining formula

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

xml-id

C10.S25.E3.m2adec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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