DLMF:28.28.E42 (Q8473): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12319 / rank
 
Normal rank
Property / Symbols used: Q12319 / qualifier
 
Defining formula:

Dsc j ( n , m , z ) Mathieu-Dsc 𝑗 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},% \NVar{z}\right)}}

\radMathieuDsc{\NVar{j}}@{\NVar{n}}{\NVar{m}}{\NVar{z}}
Property / Symbols used: Q12319 / qualifier
 
xml-id: C28.S28.E40.m1abdec

Revision as of 15:30, 2 January 2020

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DLMF:28.28.E42
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    Statements

    sinh z π 2 0 2 π cos t se n ( t , h 2 ) ce m ( t , h 2 ) sinh 2 z + sin 2 t d t = ( - 1 ) p i h β ^ n , m Dsc 1 ( n , m , z ) , 𝑧 superscript 𝜋 2 superscript subscript 0 2 𝜋 𝑡 diffop Mathieu-se 𝑛 1 𝑡 superscript 2 Mathieu-ce 𝑚 𝑡 superscript 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 imaginary-unit subscript ^ 𝛽 𝑛 𝑚 Mathieu-Dsc 1 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\dfrac{\sinh z}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\cos t% \mathrm{se}_{n}'\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right)}{{% \sinh^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p}\mathrm{i}h\widehat{\beta}_{n,m}% \mathrm{Dsc}_{1}\left(n,m,z\right),}}
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    DLMF:28.28.E42
    0 references
    Dsc j ( n , m , z ) Mathieu-Dsc 𝑗 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},% \NVar{z}\right)}}
    C28.S28.E40.m1abdec
    0 references