DLMF:13.16.E9 (Q4560): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
Normal rank
 
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
test:

W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
 
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
xml-id: C13.S14.E3.m2addec
 
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ahdec
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.m2ahdec
Property / Symbols used
 
Property / Symbols used: scaled (or Olver’s) generalized hypergeometric function / rank
 
Normal rank
Property / Symbols used: scaled (or Olver’s) generalized hypergeometric function / qualifier
 
test:

𝐅 q p ⁡ ( 𝐚 ; 𝐛 ; ) hypergeometric-bold-pFq 𝑝 𝑞 𝐚 𝐛 {\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}

\genhyperOlverF{\NVar{p}}{\NVar{q}}@{\NVar{\mathbf{a}}}{\NVar{\mathbf{b}}}{% \NVar{z}}
Property / Symbols used: scaled (or Olver’s) generalized hypergeometric function / qualifier
 
xml-id: C16.S2.E5.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ahdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1acdec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
test:

W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E3.m2addec
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.m1hdec
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.m1hdec

Latest revision as of 15:11, 2 January 2020

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Language Label Description Also known as
English
DLMF:13.16.E9
No description defined

    Statements

    test
    W κ , μ ⁡ ( z ) = e - 1 2 ⁢ z ⁢ z κ + c ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t c - 1 ⁢ 𝐅 1 2 ⁡ ( 1 2 + μ - κ , 1 2 - μ - κ c ; - t ) ⁢ d t , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 𝑐 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑐 1 hypergeometric-bold-pFq 2 1 1 2 𝜇 𝜅 1 2 𝜇 𝜅 𝑐 𝑡 𝑡 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \kappa+c}\*\int_{0}^{\infty}e^{-zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left({% \tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}-\mu-\kappa\atop c};-t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E9
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    scaled (or Olver’s) generalized hypergeometric function
    test
    𝐅 q p ⁡ ( 𝐚 ; 𝐛 ; ) hypergeometric-bold-pFq 𝑝 𝑞 𝐚 𝐛 {\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C16.S2.E5.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    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.m2addec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1hdec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1hdec
    0 references
     
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