DLMF:13.6.E5 (Q4392): 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.m2acdec

Revision as of 15:50, 2 January 2020

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DLMF:13.6.E5
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    Statements

    Defining formula
    M ⁡ ( a , a + 1 , - z ) = e - z ⁢ M ⁡ ( 1 , a + 1 , z ) = a ⁢ z - a ⁢ γ ⁡ ( a , z ) , Kummer-confluent-hypergeometric-M 𝑎 𝑎 1 𝑧 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-M 1 𝑎 1 𝑧 𝑎 superscript 𝑧 𝑎 incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle M\left(a,a+1,-z\right)=e^{-z}M\left(1,a+1,z\right% )=az^{-a}\gamma\left(a,z\right),}}
    0 references
    DLMF id
    DLMF:13.6.E5
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    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2acdec
    0 references
     
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