DLMF:13.12.E1 (Q4477): 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.m2adec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1dec

Latest revision as of 16:03, 2 January 2020

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DLMF:13.12.E1
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    Statements

    Defining formula
    M ⁡ ( a , b , z ) ⁢ M ⁡ ( - a , - b , - z ) + a ⁢ ( a - b ) ⁢ z 2 b 2 ⁢ ( 1 - b 2 ) ⁢ M ⁡ ( 1 + a , 2 + b , z ) ⁢ M ⁡ ( 1 - a , 2 - b , - z ) = 1 . Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 𝑎 𝑎 𝑏 superscript 𝑧 2 superscript 𝑏 2 1 superscript 𝑏 2 Kummer-confluent-hypergeometric-M 1 𝑎 2 𝑏 𝑧 Kummer-confluent-hypergeometric-M 1 𝑎 2 𝑏 𝑧 1 {\displaystyle{\displaystyle M\left(a,b,z\right)M\left(-a,-b,-z\right)+\frac{a% (a-b)z^{2}}{b^{2}(1-b^{2})}M\left(1+a,2+b,z\right)M\left(1-a,2-b,-z\right)=1.}}
    0 references
    DLMF id
    DLMF:13.12.E1
    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.m2adec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1dec
    0 references
     
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