DLMF:13.3.E28 (Q4362): Difference between revisions

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imported>Admin
 
imported>Admin
Property / Symbols used
 
Property / Symbols used: Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
test:

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.m2amdec

Revision as of 14:44, 2 January 2020

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DLMF:13.3.E28
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    Statements

    d n d z n ( z b - 1 e - z U ( a , b , z ) ) = ( - 1 ) n z b - n - 1 e - z U ( a - n , b - n , z ) . derivative 𝑧 𝑛 superscript 𝑧 𝑏 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 superscript 𝑧 𝑏 𝑛 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}e^{-z}U\left(a,b,z\right)\right)=(-1)^{n}z^{b-n-1}e^{-z}U\left(a-n,b-n,z% \right).}}
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    U ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    C13.S2.E6.m2amdec
    0 references