DLMF:13.2.E35 (Q4327): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Olver’s confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Olver’s confluent hypergeometric function / qualifier
 
test:

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.m2agdec

Revision as of 14:40, 2 January 2020

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DLMF:13.2.E35
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    Statements

    test
    𝒲 ⁡ { 𝐌 ⁡ ( a , b , z ) , e z ⁢ U ⁡ ( b - a , b , e ± π ⁢ i ⁢ z ) } = e ∓ b ⁢ π ⁢ i ⁢ z - b ⁢ e z / Γ ⁡ ( b - a ) , Wronskian Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑏 𝑎 𝑏 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 𝑧 superscript 𝑒 minus-or-plus 𝑏 𝜋 imaginary-unit superscript 𝑧 𝑏 superscript 𝑒 𝑧 Euler-Gamma 𝑏 𝑎 {\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),e% ^{z}U\left(b-a,b,e^{\pm\pi\mathrm{i}}z\right)\right\}=\ifrac{e^{\mp b\pi% \mathrm{i}}z^{-b}e^{z}}{\Gamma\left(b-a\right)},}}
    0 references
    DLMF id
    DLMF:13.2.E35
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2andec
    0 references
    Kummer confluent hypergeometric function
    test
    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.m2asdec
    0 references
    Olver’s confluent hypergeometric function
    test
    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.m2agdec
    0 references
     
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