DLMF:13.13.E5 (Q4482): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2addec

Revision as of 16:03, 2 January 2020

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DLMF:13.13.E5
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    Statements

    Defining formula
    e y ⁢ ( x x + y ) b - a ⁢ ∑ n = 0 ∞ ( b - a ) n ⁢ y n n ! ⁢ ( x + y ) n ⁢ M ⁡ ( a - n , b , x ) , superscript 𝑒 𝑦 superscript 𝑥 𝑥 𝑦 𝑏 𝑎 superscript subscript 𝑛 0 Pochhammer 𝑏 𝑎 𝑛 superscript 𝑦 𝑛 𝑛 superscript 𝑥 𝑦 𝑛 Kummer-confluent-hypergeometric-M 𝑎 𝑛 𝑏 𝑥 {\displaystyle{\displaystyle e^{y}\left(\frac{x}{x+y}\right)^{b-a}\sum_{n=0}^{% \infty}\frac{{\left(b-a\right)_{n}}y^{n}}{n!(x+y)^{n}}\*M\left(a-n,b,x\right),}}
    0 references
    DLMF id
    DLMF:13.13.E5
    0 references
    constraint
    ℜ ⁡ ( ( y + x ) / x ) > 1 2 𝑦 𝑥 𝑥 1 2 {\displaystyle{\displaystyle\Re((y+x)/x)>\frac{1}{2}}}
    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.m2addec
    0 references
     
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