DLMF:10.22.E2 (Q3374): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1adec

Revision as of 14:48, 2 January 2020

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DLMF:10.22.E2
No description defined

    Statements

    test
    ∫ z ν ⁢ 𝒞 ν ⁡ ( z ) ⁢ d z = π 1 2 ⁢ 2 ν - 1 ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ z ⁢ ( 𝒞 ν ⁡ ( z ) ⁢ 𝐇 ν - 1 ⁡ ( z ) - 𝒞 ν - 1 ⁡ ( z ) ⁢ 𝐇 ν ⁡ ( z ) ) , superscript 𝑧 𝜈 cylinder-function 𝜈 𝑧 𝑧 superscript 𝜋 1 2 superscript 2 𝜈 1 Euler-Gamma 𝜈 1 2 𝑧 cylinder-function 𝜈 𝑧 Struve-H 𝜈 1 𝑧 cylinder-function 𝜈 1 𝑧 Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\int z^{\nu}\mathscr{C}_{\nu}\left(z\right)\mathrm% {d}z=\pi^{\frac{1}{2}}2^{\nu-1}\Gamma\left(\nu+\tfrac{1}{2}\right)\*z\left(% \mathscr{C}_{\nu}\left(z\right)\mathbf{H}_{\nu-1}\left(z\right)-\mathscr{C}_{% \nu-1}\left(z\right)\mathbf{H}_{\nu}\left(z\right)\right),}}
    0 references
    DLMF id
    DLMF:10.22.E2
    0 references
    constraint
    ν ≠ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\tfrac{1}{2}}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Struve function
    test
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q11430
    test
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
     
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