DLMF:13.4.E13 (Q4376): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Olver’s confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Olver’s confluent hypergeometric function / qualifier
 
Defining formula:

𝐌 ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}

\OlverconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: Olver’s confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E3.m2ahdec

Revision as of 15:48, 2 January 2020

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DLMF:13.4.E13
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    Statements

    Defining formula
    𝐌 ⁡ ( a , b , z ) = z 1 - b 2 ⁢ π ⁢ i ⁢ ∫ - ∞ ( 0 + , 1 + ) e z ⁢ t ⁢ t - b ⁢ ( 1 - 1 t ) - a ⁢ d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 superscript 𝑧 1 𝑏 2 𝜋 imaginary-unit superscript subscript limit-from 0 limit-from 1 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑏 superscript 1 1 𝑡 𝑎 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{z^{1-b}}{2\pi% \mathrm{i}}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}\!\left(1-\frac{1}{t}\right)^{-% a}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E13
    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
    Olver’s confluent hypergeometric function
    Defining formula
    𝐌 ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2ahdec
    0 references
     
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