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

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

{\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),}}

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DLMF:13.8.E8

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

C2.S1.E3.m2acdec

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

C5.S2.E1.m2acdec

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

C13.S2.E6.m2abdec

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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