DLMF:28.24.E4 (Q8401): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
Defining formula:

J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2acdec

Revision as of 15:11, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.24.E4
No description defined

    Statements

    Ms 2 m + 1 ( j ) ( z , h ) = ( - 1 ) m = 0 ( - 1 ) B 2 + 1 2 m + 1 ( h 2 ) B 2 s + 1 2 m + 1 ( h 2 ) ( J - s ( h e - z ) 𝒞 + s + 1 ( j ) ( h e z ) - J + s + 1 ( h e - z ) 𝒞 - s ( j ) ( h e z ) ) , modified-Mathieu-Ms 𝑗 2 𝑚 1 𝑧 superscript 1 𝑚 superscript subscript 0 superscript 1 superscript subscript 𝐵 2 1 2 𝑚 1 superscript 2 superscript subscript 𝐵 2 𝑠 1 2 𝑚 1 superscript 2 Bessel-J 𝑠 superscript 𝑒 𝑧 superscript subscript 𝒞 𝑠 1 𝑗 superscript 𝑒 𝑧 Bessel-J 𝑠 1 superscript 𝑒 𝑧 superscript subscript 𝒞 𝑠 𝑗 superscript 𝑒 𝑧 {\displaystyle{\displaystyle{\mathrm{Ms}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m% }\sum_{\ell=0}^{\infty}(-1)^{\ell}\frac{B_{2\ell+1}^{2m+1}(h^{2})}{B_{2s+1}^{2% m+1}(h^{2})}\left(J_{\ell-s}\left(he^{-z}\right){\cal C}_{\ell+s+1}^{(j)}(he^{% z})-J_{\ell+s+1}\left(he^{-z}\right){\cal C}_{\ell-s}^{(j)}(he^{z})\right),}}
    0 references
    DLMF:28.24.E4
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2acdec
    0 references