DLMF:11.4.E21 (Q3953): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2akdec
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.m2aodec
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.m1sdec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11497 / qualifier
 
xml-id: C11.S1.XMD5.m1cdec

Latest revision as of 14:41, 2 January 2020

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DLMF:11.4.E21
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    Statements

    𝐇 0 ( z ) = 4 π k = 0 J 2 k + 1 ( z ) 2 k + 1 = 2 k = 0 ( - 1 ) k J k + 1 2 2 ( 1 2 z ) , Struve-H 0 𝑧 4 𝜋 superscript subscript 𝑘 0 Bessel-J 2 𝑘 1 𝑧 2 𝑘 1 2 superscript subscript 𝑘 0 superscript 1 𝑘 Bessel-J 𝑘 1 2 2 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{0}\left(z\right)=\frac{4}{\pi}\sum_{k=% 0}^{\infty}\frac{J_{2k+1}\left(z\right)}{2k+1}=2\sum_{k=0}^{\infty}(-1)^{k}{J_% {k+\frac{1}{2}}^{2}}\left(\tfrac{1}{2}z\right),}}
    0 references
    DLMF:11.4.E21
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2addec
    0 references
    𝐇 ν ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C11.S2.E1.m2akdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aodec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C11.S1.XMD2.m1sdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C11.S1.XMD5.m1cdec
    0 references