DLMF:28.24.E2 (Q8399): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec

Revision as of 15:10, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.24.E2
No description defined

    Statements

    Defining formula
    ε s ⁢ Mc 2 ⁢ m ( j ) ⁡ ( z , h ) = ( - 1 ) m ⁢ ∑ ℓ = 0 ∞ ( - 1 ) ℓ ⁢ A 2 ⁢ ℓ 2 ⁢ m ⁢ ( h 2 ) A 2 ⁢ s 2 ⁢ m ⁢ ( h 2 ) ⁢ ( J ℓ - s ⁡ ( h ⁢ e - z ) ⁢ 𝒞 ℓ + s ( j ) ⁢ ( h ⁢ e z ) + J ℓ + s ⁡ ( h ⁢ e - z ) ⁢ 𝒞 ℓ - s ( j ) ⁢ ( h ⁢ e z ) ) , subscript 𝜀 𝑠 modified-Mathieu-Mc 𝑗 2 𝑚 𝑧 ℎ superscript 1 𝑚 superscript subscript ℓ 0 superscript 1 ℓ superscript subscript 𝐴 2 ℓ 2 𝑚 superscript ℎ 2 superscript subscript 𝐴 2 𝑠 2 𝑚 superscript ℎ 2 Bessel-J ℓ 𝑠 ℎ superscript 𝑒 𝑧 superscript subscript 𝒞 ℓ 𝑠 𝑗 ℎ superscript 𝑒 𝑧 Bessel-J ℓ 𝑠 ℎ superscript 𝑒 𝑧 superscript subscript 𝒞 ℓ 𝑠 𝑗 ℎ superscript 𝑒 𝑧 {\displaystyle{\displaystyle\varepsilon_{s}{\mathrm{Mc}^{(j)}_{2m}}\left(z,h% \right)=(-1)^{m}\sum_{\ell=0}^{\infty}(-1)^{\ell}\frac{A_{2\ell}^{2m}(h^{2})}{% A_{2s}^{2m}(h^{2})}\left(J_{\ell-s}\left(he^{-z}\right){\cal C}_{\ell+s}^{(j)}% (he^{z})+J_{\ell+s}\left(he^{-z}\right){\cal C}_{\ell-s}^{(j)}(he^{z})\right),}}
    0 references
    DLMF id
    DLMF:28.24.E2
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8399&oldid=55074"