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DLMF:13.6.E21 - MaRDI portal

DLMF:13.6.E21 (Q5105)

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DLMF:13.6.E21
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    Statements

    DLMF defining formula
    U ⁡ ( a , b , z ) = z - a ⁢ F 0 2 ⁡ ( a , a - b + 1 ; - ; - z - 1 ) . Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 Gauss-hypergeometric-pFq 2 0 𝑎 𝑎 𝑏 1 superscript 𝑧 1 {\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}{{}_{2}F_{0}}\left(a,a-% b+1;-;-z^{-1}\right).}}
    0 references
    Symbols used
    alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
    DLMF defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1adec
    0 references
    Kummer confluent hypergeometric function
    DLMF 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.m2akdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1tdec
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    Identifiers

     
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