DLMF:11.4.E23 (Q3955): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Struve function / rank
 
Normal rank
Property / Symbols used: Struve function / qualifier
 
Defining formula:

𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\StruveH{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Struve function / qualifier
 
xml-id: C11.S2.E1.m2amdec

Revision as of 14:41, 2 January 2020

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DLMF:11.4.E23
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    Statements

    Defining formula
    𝐇 ν - 1 ⁡ ( z ) + 𝐇 ν + 1 ⁡ ( z ) = 2 ⁢ ν z ⁢ 𝐇 ν ⁡ ( z ) + ( 1 2 ⁢ z ) ν π ⁢ Γ ⁡ ( ν + 3 2 ) , Struve-H 𝜈 1 𝑧 Struve-H 𝜈 1 𝑧 2 𝜈 𝑧 Struve-H 𝜈 𝑧 superscript 1 2 𝑧 𝜈 𝜋 Euler-Gamma 𝜈 3 2 {\displaystyle{\displaystyle\mathbf{H}_{\nu-1}\left(z\right)+\mathbf{H}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{H}_{\nu}\left(z\right)+\frac{(\tfrac{1}{% 2}z)^{\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)},}}
    0 references
    DLMF id
    DLMF:11.4.E23
    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.m2acdec
    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.m2amdec
    0 references
     
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