DLMF:13.13.E12 (Q4489): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
Defining formula:

U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

\KummerconfhyperU@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E6.m2aedec

Revision as of 16:04, 2 January 2020

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DLMF:13.13.E12
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    Statements

    Defining formula
    e y ⁢ ( x + y x ) 1 - b ⁢ ∑ n = 0 ∞ ( - y ) n n ! ⁢ x n ⁢ U ⁡ ( a - n , b - n , x ) , superscript 𝑒 𝑦 superscript 𝑥 𝑦 𝑥 1 𝑏 superscript subscript 𝑛 0 superscript 𝑦 𝑛 𝑛 superscript 𝑥 𝑛 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑛 𝑥 {\displaystyle{\displaystyle e^{y}\left(\frac{x+y}{x}\right)^{1-b}\sum_{n=0}^{% \infty}\frac{(-y)^{n}}{n!x^{n}}U\left(a-n,b-n,x\right),}}
    0 references
    DLMF id
    DLMF:13.13.E12
    0 references
    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
    0 references
    Symbols used
    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.m2aedec
    0 references
     
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