DLMF:13.6.E19 (Q4406): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11333 / rank
 
Normal rank
Property / Symbols used: Q11333 / qualifier
 
Defining formula:

L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11333 / qualifier
 
xml-id: C18.S3.T1.t1.r12.m2adec

Revision as of 15:53, 2 January 2020

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DLMF:13.6.E19
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    Statements

    Defining formula
    U ⁡ ( - n , α + 1 , z ) = ( - 1 ) n ⁢ ( α + 1 ) n ⁢ M ⁡ ( - n , α + 1 , z ) = ( - 1 ) n ⁢ n ! ⁢ L n ( α ) ⁡ ( z ) . Kummer-confluent-hypergeometric-U 𝑛 𝛼 1 𝑧 superscript 1 𝑛 Pochhammer 𝛼 1 𝑛 Kummer-confluent-hypergeometric-M 𝑛 𝛼 1 𝑧 superscript 1 𝑛 𝑛 Laguerre-polynomial-L 𝛼 𝑛 𝑧 {\displaystyle{\displaystyle U\left(-n,\alpha+1,z\right)=(-1)^{n}{\left(\alpha% +1\right)_{n}}M\left(-n,\alpha+1,z\right)=(-1)^{n}n!L^{(\alpha)}_{n}\left(z% \right).}}
    0 references
    DLMF id
    DLMF:13.6.E19
    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.m2ajdec
    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.m2aidec
    0 references
    Q11333
    Defining formula
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2adec
    0 references
     
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