DLMF:13.4.E8 (Q4371): Difference between revisions

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

Revision as of 15:46, 2 January 2020

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DLMF:13.4.E8
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) = z c - a ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t c - 1 ⁢ 𝐅 1 2 ⁡ ( a , a - b + 1 ; c ; - t ) ⁢ d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑐 𝑎 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑐 1 hypergeometric-bold-pFq 2 1 𝑎 𝑎 𝑏 1 𝑐 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=z^{c-a}\*\int_{0}^{\infty}e^{% -zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left(a,a-b+1;c;-t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E8
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}
    0 references
    Symbols used
    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.m2addec
    0 references
     
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