DLMF:13.2.E34 (Q4326): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aedec

Revision as of 15:40, 2 January 2020

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DLMF:13.2.E34
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    Statements

    Defining formula
    𝒲 ⁡ { 𝐌 ⁡ ( a , b , z ) , U ⁡ ( a , b , z ) } = - z - b ⁢ e z / Γ ⁡ ( a ) , Wronskian Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑏 superscript 𝑒 𝑧 Euler-Gamma 𝑎 {\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),U% \left(a,b,z\right)\right\}=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a\right)},}}
    0 references
    DLMF id
    DLMF:13.2.E34
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2amdec
    0 references
    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.m2ardec
    0 references
    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.m2afdec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
     
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