DLMF:13.14.E27 (Q4519): 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.m2apdec

Revision as of 15:07, 2 January 2020

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DLMF:13.14.E27
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    Statements

    test
    𝒲 ⁡ { M κ , μ ⁡ ( z ) , W - κ , μ ⁡ ( e ± π ⁢ i ⁢ z ) } = Γ ⁡ ( 1 + 2 ⁢ μ ) Γ ⁡ ( 1 2 + μ + κ ) ⁢ e ∓ ( 1 2 + μ ) ⁢ π ⁢ i , Wronskian Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 𝑧 Euler-Gamma 1 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 superscript 𝑒 minus-or-plus 1 2 𝜇 𝜋 imaginary-unit {\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{\pm\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1+2% \mu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{\mp(\frac{1}{2}+\mu)% \pi\mathrm{i}},}}
    0 references
    DLMF id
    DLMF:13.14.E27
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ajdec
    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.m2aldec
    0 references
    Whittaker confluent hypergeometric function
    test
    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.m2aodec
    0 references
    Q10865
    test
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2apdec
    0 references
     
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