DLMF:13.3.E16 (Q4350): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1odec

Latest revision as of 14:42, 2 January 2020

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DLMF:13.3.E16
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    Statements

    test
    d n d z n ⁡ M ⁡ ( a , b , z ) = ( a ) n ( b ) n ⁢ M ⁡ ( a + n , b + n , z ) , derivative 𝑧 𝑛 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 Pochhammer 𝑎 𝑛 Pochhammer 𝑏 𝑛 Kummer-confluent-hypergeometric-M 𝑎 𝑛 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}M\left(a% ,b,z\right)=\frac{{\left(a\right)_{n}}}{{\left(b\right)_{n}}}M\left(a+n,b+n,z% \right),}}
    0 references
    DLMF id
    DLMF:13.3.E16
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    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    test
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2ahdec
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    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aadec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1dec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1odec
    0 references
     
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