DLMF:13.3.E13 (Q4347): 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.m2afdec

Revision as of 15:42, 2 January 2020

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DLMF:13.3.E13
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    Statements

    Defining formula
    ( a + 1 ) ⁢ z ⁢ M ⁡ ( a + 2 , b + 2 , z ) + ( b + 1 ) ⁢ ( b - z ) ⁢ M ⁡ ( a + 1 , b + 1 , z ) - b ⁢ ( b + 1 ) ⁢ M ⁡ ( a , b , z ) = 0 , 𝑎 1 𝑧 Kummer-confluent-hypergeometric-M 𝑎 2 𝑏 2 𝑧 𝑏 1 𝑏 𝑧 Kummer-confluent-hypergeometric-M 𝑎 1 𝑏 1 𝑧 𝑏 𝑏 1 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 0 {\displaystyle{\displaystyle(a+1)zM\left(a+2,b+2,z\right)+(b+1)(b-z)M\left(a+1% ,b+1,z\right)-b(b+1)M\left(a,b,z\right)=0,}}
    0 references
    DLMF id
    DLMF:13.3.E13
    0 references
    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.m2afdec
    0 references
     
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