DLMF:11.4.E14 (Q3946): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1adec

Latest revision as of 14:39, 2 January 2020

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DLMF:11.4.E14
No description defined

    Statements

    Defining formula
    𝐇 ν ⁡ ( z ) = 2 ⁢ ( 1 2 ⁢ z ) ν + 1 π ⁢ Γ ⁡ ( ν + 3 2 ) ⁢ ( 1 + ϑ ) , Struve-H 𝜈 𝑧 2 superscript 1 2 𝑧 𝜈 1 𝜋 Euler-Gamma 𝜈 3 2 1 italic-ϑ {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2% }z)^{\nu+1}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)}(1+\vartheta),}}
    0 references
    DLMF id
    DLMF:11.4.E14
    0 references
    constraint
    ν ≠ - 3 2 , - 5 2 , - 7 2 , … 𝜈 3 2 5 2 7 2 … {\displaystyle{\displaystyle\nu\neq-\tfrac{3}{2},-\tfrac{5}{2},-\tfrac{7}{2},% \dots}}
    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.m2adec
    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.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1ldec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1adec
    0 references
     
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