DLMF:13.14.E30 (Q4522): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10865 / rank
 
Normal rank
Property / Symbols used: Q10865 / qualifier
 
Defining formula:

𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}

\Wronskian
Property / Symbols used: Q10865 / qualifier
 
xml-id: C1.S13.Px2.p1.m3aedec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2ajdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1acdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ardec

Latest revision as of 16:07, 2 January 2020

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DLMF:13.14.E30
No description defined

    Statements

    Defining formula
    𝒲 ⁡ { W κ , μ ⁡ ( z ) , W - κ , μ ⁡ ( e ± π ⁢ i ⁢ z ) } = e ∓ κ ⁢ π ⁢ i . Wronskian Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 𝑧 superscript 𝑒 minus-or-plus 𝜅 𝜋 imaginary-unit {\displaystyle{\displaystyle\mathscr{W}\left\{W_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{\pm\pi\mathrm{i}}z\right)\right\}=e^{\mp\kappa\pi\mathrm{% i}}.}}
    0 references
    DLMF id
    DLMF:13.14.E30
    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.m2ardec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ardec
    0 references
     
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