DLMF:13.6.E20 (Q4407)

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DLMF:13.6.E20
No description defined

    Statements

    Defining formula
    U ⁡ ( - n , z - n + 1 , a ) = ( - z ) n ⁢ M ⁡ ( - n , z - n + 1 , a ) = a n ⁢ C n ⁡ ( z ; a ) . Kummer-confluent-hypergeometric-U 𝑛 𝑧 𝑛 1 𝑎 Pochhammer 𝑧 𝑛 Kummer-confluent-hypergeometric-M 𝑛 𝑧 𝑛 1 𝑎 superscript 𝑎 𝑛 Charlier-polynomial-C 𝑛 𝑧 𝑎 {\displaystyle{\displaystyle U\left(-n,z-n+1,a\right)={\left(-z\right)_{n}}M% \left(-n,z-n+1,a\right)=a^{n}C_{n}\left(z;a\right).}}
    0 references
    DLMF id
    DLMF:13.6.E20
    0 references
    Symbols used
    Q11565
    Defining formula
    C n ⁡ ( x ; a ) Charlier-polynomial-C 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle C_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}
    xml-id
    C18.S19.T1.t1.r5.m2adec
    0 references
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ 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.m2akdec
    0 references
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2ajdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
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    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1ddec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1sdec
    0 references
     
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