DLMF:13.7.E3 (Q4411): 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.m2adec

Revision as of 15:54, 2 January 2020

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DLMF:13.7.E3
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) ∼ z - a ⁢ ∑ s = 0 ∞ ( a ) s ⁢ ( a - b + 1 ) s s ! ⁢ ( - z ) - s , asymptotic-expansion Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑠 0 Pochhammer 𝑎 𝑠 Pochhammer 𝑎 𝑏 1 𝑠 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle U\left(a,b,z\right)\sim z^{-a}\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s},}}
    0 references
    DLMF id
    DLMF:13.7.E3
    0 references
    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
    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.m2adec
    0 references
     
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