DLMF:13.15.E26 (Q4551): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2akdec

Revision as of 16:10, 2 January 2020

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DLMF:13.15.E26
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    Statements

    Defining formula
    ( z ⁢ d d z ⁡ z ) n ⁢ ( e - 1 2 ⁢ z ⁢ z κ - 1 ⁢ W κ , μ ⁡ ( z ) ) = ( - 1 ) n ⁢ e - 1 2 ⁢ z ⁢ z κ + n - 1 ⁢ W κ + n , μ ⁡ ( z ) . superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 1 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 1 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 𝑛 1 Whittaker-confluent-hypergeometric-W 𝜅 𝑛 𝜇 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(e^{-\frac{1}{2}z}z^{\kappa-1}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n% }e^{-\frac{1}{2}z}z^{\kappa+n-1}W_{\kappa+n,\mu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.15.E26
    0 references
    Symbols used
    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2aldec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2akdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1kdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ydec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2akdec
    0 references
     
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