DLMF:13.3.E21 (Q4355): Difference between revisions

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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
 
test:

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.m2amdec

Revision as of 14:43, 2 January 2020

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DLMF:13.3.E21
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    Statements

    test
    d n d z n ⁡ ( z b - 1 ⁢ e - z ⁢ M ⁡ ( a , b , z ) ) = ( b - n ) n ⁢ z b - n - 1 ⁢ e - z ⁢ M ⁡ ( a - n , b - n , z ) . derivative 𝑧 𝑛 superscript 𝑧 𝑏 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 Pochhammer 𝑏 𝑛 𝑛 superscript 𝑧 𝑏 𝑛 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑛 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}e^{-z}M\left(a,b,z\right)\right)={\left(b-n\right)_{n}}z^{b-n-1}e^{-z}M% \left(a-n,b-n,z\right).}}
    0 references
    DLMF id
    DLMF:13.3.E21
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    test
    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.m2amdec
    0 references
     
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