DLMF:13.2.E7 (Q4297): Difference between revisions

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‎Changed an Item: Add constraint
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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.m2aadec

Revision as of 15:35, 2 January 2020

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DLMF:13.2.E7
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    Statements

    Defining formula
    U ⁡ ( - m , b , z ) = ( - 1 ) m ⁢ ( b ) m ⁢ M ⁡ ( - m , b , z ) = ( - 1 ) m ⁢ ∑ s = 0 m ( m s ) ⁢ ( b + s ) m - s ⁢ ( - z ) s . Kummer-confluent-hypergeometric-U 𝑚 𝑏 𝑧 superscript 1 𝑚 Pochhammer 𝑏 𝑚 Kummer-confluent-hypergeometric-M 𝑚 𝑏 𝑧 superscript 1 𝑚 superscript subscript 𝑠 0 𝑚 binomial 𝑚 𝑠 Pochhammer 𝑏 𝑠 𝑚 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle U\left(-m,b,z\right)=(-1)^{m}{\left(b\right)_{m}}% M\left(-m,b,z\right)=(-1)^{m}\sum_{s=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{s}{\left% (b+s\right)_{m-s}}(-z)^{s}.}}
    0 references
    DLMF id
    DLMF:13.2.E7
    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.m2acdec
    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.m2aadec
    0 references
     
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