DLMF:13.15.E15 (Q4540): 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
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: Q11559 / rank
 
Normal rank
Property / Symbols used: Q11559 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11559 / qualifier
 
xml-id: C13.S1.XMD2.m1dec
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.m1ndec

Latest revision as of 15:08, 2 January 2020

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English
DLMF:13.15.E15
No description defined

    Statements

    test
    d n d z n ⁡ ( e 1 2 ⁢ z ⁢ z μ - 1 2 ⁢ M κ , μ ⁡ ( z ) ) = ( - 1 ) n ⁢ ( - 2 ⁢ μ ) n ⁢ e 1 2 ⁢ z ⁢ z μ - 1 2 ⁢ ( n + 1 ) ⁢ M κ - 1 2 ⁢ n , μ - 1 2 ⁢ n ⁡ ( z ) , derivative 𝑧 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 superscript 1 𝑛 Pochhammer 2 𝜇 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 𝑛 1 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {\frac{1}{2}z}z^{\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{% \left(-2\mu\right)_{n}}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}M_{\kappa-\frac% {1}{2}n,\mu-\frac{1}{2}n}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.15.E15
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2agdec
    0 references
    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.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    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.m1ndec
    0 references
     
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