DLMF:11.4.E28 (Q3960): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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
 
Defining formula:

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.m2audec

Revision as of 14:42, 2 January 2020

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DLMF:11.4.E28
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    Statements

    Defining formula
    d d z ⁡ ( z - ν ⁢ 𝐇 ν ⁡ ( z ) ) = 2 - ν π ⁢ Γ ⁡ ( ν + 3 2 ) - z - ν ⁢ 𝐇 ν + 1 ⁡ ( z ) , derivative 𝑧 superscript 𝑧 𝜈 Struve-H 𝜈 𝑧 superscript 2 𝜈 𝜋 Euler-Gamma 𝜈 3 2 superscript 𝑧 𝜈 Struve-H 𝜈 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\left(z^{-\nu}% \mathbf{H}_{\nu}\left(z\right)\right)=\frac{2^{-\nu}}{\sqrt{\pi}\Gamma\left(% \nu+\tfrac{3}{2}\right)}-z^{-\nu}\mathbf{H}_{\nu+1}\left(z\right),}}
    0 references
    DLMF id
    DLMF:11.4.E28
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    Struve function
    Defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2apdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2audec
    0 references
     
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