DLMF:31.8.E2 (Q9037): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
test:

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.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.m3adec
Property / Symbols used
 
Property / Symbols used: Q12457 / rank
 
Normal rank
Property / Symbols used: Q12457 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12457 / qualifier
 
xml-id: C31.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12485 / rank
 
Normal rank
Property / Symbols used: Q12485 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12485 / qualifier
 
xml-id: C31.S1.XMD13.m1dec
Property / Symbols used
 
Property / Symbols used: Q12483 / rank
 
Normal rank
Property / Symbols used: Q12483 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12483 / qualifier
 
xml-id: C31.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q12461 / rank
 
Normal rank
Property / Symbols used: Q12461 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12461 / qualifier
 
xml-id: C31.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q12487 / rank
 
Normal rank
Property / Symbols used: Q12487 / qualifier
 
test:

λ = - 4 ⁢ q 𝜆 4 𝑞 {\displaystyle{\displaystyle\lambda=-4q}}

\lambda=-4q
Property / Symbols used: Q12487 / qualifier
 
xml-id: C31.S8.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12488 / rank
 
Normal rank
Property / Symbols used: Q12488 / qualifier
 
test:

Ψ g , N ⁢ ( λ , z ) subscript Ψ 𝑔 𝑁 𝜆 𝑧 {\displaystyle{\displaystyle\Psi_{g,N}(\lambda,z)}}

\Psi_{g,N}(\lambda,z)
Property / Symbols used: Q12488 / qualifier
 
xml-id: C31.S8.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12489 / rank
 
Normal rank
Property / Symbols used: Q12489 / qualifier
 
test:

g 𝑔 {\displaystyle{\displaystyle g}}

g
Property / Symbols used: Q12489 / qualifier
 
xml-id: C31.S8.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12490 / rank
 
Normal rank
Property / Symbols used: Q12490 / qualifier
 
test:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q12490 / qualifier
 
xml-id: C31.S8.XMD4.m1dec

Latest revision as of 13:33, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:31.8.E2
No description defined

    Statements

    test
    w ± ⁢ ( 𝐦 ; λ ; z ) = Ψ g , N ⁢ ( λ , z ) ⁢ exp ⁡ ( ± i ⁢ ν ⁢ ( λ ) 2 ⁢ ∫ z 0 z t m 1 ⁢ ( t - 1 ) m 2 ⁢ ( t - a ) m 3 ⁢ d t Ψ g , N ⁢ ( λ , t ) ⁢ t ⁢ ( t - 1 ) ⁢ ( t - a ) ) subscript 𝑤 plus-or-minus 𝐦 𝜆 𝑧 subscript Ψ 𝑔 𝑁 𝜆 𝑧 plus-or-minus 𝑖 𝜈 𝜆 2 superscript subscript subscript 𝑧 0 𝑧 superscript 𝑡 subscript 𝑚 1 superscript 𝑡 1 subscript 𝑚 2 superscript 𝑡 𝑎 subscript 𝑚 3 𝑡 subscript Ψ 𝑔 𝑁 𝜆 𝑡 𝑡 𝑡 1 𝑡 𝑎 {\displaystyle{\displaystyle w_{\pm}(\mathbf{m};\lambda;z)=\sqrt{\Psi_{g,N}(% \lambda,z)}\*\exp\left(\pm\frac{i\nu(\lambda)}{2}\int_{z_{0}}^{z}\frac{t^{m_{1% }}(t-1)^{m_{2}}(t-a)^{m_{3}}\mathrm{d}t}{\Psi_{g,N}(\lambda,t)\sqrt{t(t-1)(t-a% )}}\right)}}
    0 references
    DLMF id
    DLMF:31.8.E2
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q12457
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1dec
    0 references
    Q12485
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C31.S1.XMD13.m1dec
    0 references
    Q12483
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C31.S1.XMD4.m1adec
    0 references
    Q12461
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1dec
    0 references
    Q12487
    test
    λ = - 4 ⁢ q 𝜆 4 𝑞 {\displaystyle{\displaystyle\lambda=-4q}}
    xml-id
    C31.S8.XMD1.m1dec
    0 references
    Q12488
    test
    Ψ g , N ⁢ ( λ , z ) subscript Ψ 𝑔 𝑁 𝜆 𝑧 {\displaystyle{\displaystyle\Psi_{g,N}(\lambda,z)}}
    xml-id
    C31.S8.XMD2.m1dec
    0 references
    Q12489
    test
    g 𝑔 {\displaystyle{\displaystyle g}}
    xml-id
    C31.S8.XMD3.m1dec
    0 references
    Q12490
    test
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C31.S8.XMD4.m1dec
    0 references
     
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