DLMF:18.23.E1 (Q5902): Difference between revisions

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Property / constraint
 

x = 0 , 1 , , N 𝑥 0 1 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}

x=0,1,\dots,N
Property / constraint: x = 0 , 1 , , N 𝑥 0 1 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}} / rank
 
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Revision as of 17:02, 30 December 2019

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DLMF:18.23.E1
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    Statements

    F 1 1 ( - x α + 1 ; - z ) F 1 1 ( x - N β + 1 ; z ) = n = 0 N ( - N ) n ( β + 1 ) n n ! Q n ( x ; α , β , N ) z n , Kummer-confluent-hypergeometric-M-as-1F1 𝑥 𝛼 1 𝑧 Kummer-confluent-hypergeometric-M-as-1F1 𝑥 𝑁 𝛽 1 𝑧 superscript subscript 𝑛 0 𝑁 Pochhammer 𝑁 𝑛 Pochhammer 𝛽 1 𝑛 𝑛 Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 superscript 𝑧 𝑛 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left({-x\atop\alpha+1};-z\right){{}_% {1}F_{1}}\left({x-N\atop\beta+1};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)% _{n}}}{{\left(\beta+1\right)_{n}}n!}Q_{n}\left(x;\alpha,\beta,N\right)z^{n},}}
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    x = 0 , 1 , , N 𝑥 0 1 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}
    0 references