DLMF:11.7.E2 (Q3991): Difference between revisions

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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
 
test:

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.m2adec

Revision as of 13:48, 2 January 2020

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DLMF:11.7.E2
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    Statements

    test
    ∫ z - ν ⁢ 𝐇 ν + 1 ⁡ ( z ) ⁢ d z = - z - ν ⁢ 𝐇 ν ⁡ ( z ) + 2 - ν ⁢ z π ⁢ Γ ⁡ ( ν + 3 2 ) , superscript 𝑧 𝜈 Struve-H 𝜈 1 𝑧 𝑧 superscript 𝑧 𝜈 Struve-H 𝜈 𝑧 superscript 2 𝜈 𝑧 𝜋 Euler-Gamma 𝜈 3 2 {\displaystyle{\displaystyle\int z^{-\nu}\mathbf{H}_{\nu+1}\left(z\right)% \mathrm{d}z=-z^{-\nu}\mathbf{H}_{\nu}\left(z\right)+\frac{2^{-\nu}z}{\sqrt{\pi% }\Gamma\left(\nu+\tfrac{3}{2}\right)},}}
    0 references
    DLMF id
    DLMF:11.7.E2
    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.m2aadec
    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
     
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