DLMF:14.23.E7 (Q4953): 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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11630 / rank
 
Normal rank
Property / Symbols used: Q11630 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: Q11630 / qualifier
 
xml-id: C14.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1fdec

Latest revision as of 13:40, 2 January 2020

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English
DLMF:14.23.E7
No description defined

    Statements

    Defining formula
    𝖰 ^ - 1 2 + i ⁢ τ - μ ⁡ ( x ) = 1 2 ⁢ e 3 ⁢ μ ⁢ π ⁢ i / 2 ⁢ Q - 1 2 + i ⁢ τ - μ ⁡ ( x - i ⁢ 0 ) + 1 2 ⁢ e - 3 ⁢ μ ⁢ π ⁢ i / 2 ⁢ Q - 1 2 - i ⁢ τ - μ ⁡ ( x + i ⁢ 0 ) . Ferrers-conical-legendre-Q-hat 𝜇 1 2 𝑖 𝜏 𝑥 1 2 superscript 𝑒 3 𝜇 𝜋 𝑖 2 Legendre-Q-second-kind 𝜇 1 2 𝑖 𝜏 𝑥 𝑖 0 1 2 superscript 𝑒 3 𝜇 𝜋 𝑖 2 Legendre-Q-second-kind 𝜇 1 2 𝑖 𝜏 𝑥 𝑖 0 {\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+i\tau}% \left(x\right)=\tfrac{1}{2}e^{3\mu\pi i/2}Q^{-\mu}_{-\frac{1}{2}+i\tau}\left(x% -i0\right)+\tfrac{1}{2}e^{-3\mu\pi i/2}Q^{-\mu}_{-\frac{1}{2}-i\tau}\left(x+i0% \right).}}
    0 references
    DLMF id
    DLMF:14.23.E7
    0 references
    Symbols used
    conical function
    Defining formula
    𝖰 ^ - 1 2 + i ⁢ τ - μ ⁡ ( x ) Ferrers-conical-legendre-Q-hat 𝜇 1 2 𝑖 𝜏 𝑥 {\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1% }{2}+i\tau}}\left(\NVar{x}\right)}}
    xml-id
    C14.S20.E2.m2adec
    0 references
    Q11470
    Defining formula
    Q ν μ ⁡ ( z ) Legendre-Q-second-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1fdec
    0 references
    Q11630
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C14.S1.XMD3.m1dec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1fdec
    0 references
     
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