DLMF:14.20.E12 (Q4933): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1qdec

Revision as of 13:34, 2 January 2020

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DLMF:14.20.E12
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    Statements

    Defining formula
    g ⁢ ( x ) = ∫ 0 ∞ P - 1 2 + i ⁢ τ μ ⁡ ( x ) ⁢ f ⁢ ( τ ) ⁢ d τ . 𝑔 𝑥 superscript subscript 0 Legendre-P-first-kind 𝜇 1 2 𝑖 𝜏 𝑥 𝑓 𝜏 𝜏 {\displaystyle{\displaystyle g(x)=\int_{0}^{\infty}P^{\mu}_{-\frac{1}{2}+i\tau% }\left(x\right)f(\tau)\mathrm{d}\tau.}}
    0 references
    DLMF id
    DLMF:14.20.E12
    0 references
    Symbols used
    Q11481
    Defining formula
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ardec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1qdec
    0 references
     
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