DLMF:13.2.E8 (Q4298): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
 
Defining formula:

M ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

\KummerconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E2.m2addec

Revision as of 15:35, 2 January 2020

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DLMF:13.2.E8
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    U ( a , a + n + 1 , z ) = ( - 1 ) n ( 1 - a - n ) n z a + n M ( - n , 1 - a - n , z ) = z - a s = 0 n ( n s ) ( a ) s z - s . Kummer-confluent-hypergeometric-U 𝑎 𝑎 𝑛 1 𝑧 superscript 1 𝑛 Pochhammer 1 𝑎 𝑛 𝑛 superscript 𝑧 𝑎 𝑛 Kummer-confluent-hypergeometric-M 𝑛 1 𝑎 𝑛 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑠 0 𝑛 binomial 𝑛 𝑠 Pochhammer 𝑎 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-% n\right)_{n}}}{z^{a+n}}M\left(-n,1-a-n,z\right)=z^{-a}\sum_{s=0}^{n}\genfrac{(% }{)}{0.0pt}{}{n}{s}{\left(a\right)_{s}}z^{-s}.}}
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    DLMF:13.2.E8
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    M ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    C13.S2.E2.m2addec
    0 references