DLMF:28.28.E15 (Q8439): Difference between revisions

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Property / Symbols used: Q12283 / rank
 
Normal rank
Property / Symbols used: Q12283 / qualifier
 
Defining formula:

ce n ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

\Mathieuce{\NVar{n}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q12283 / qualifier
 
xml-id: C28.S2.SS6.p1.m7acdec

Revision as of 15:21, 2 January 2020

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DLMF:28.28.E15
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    0 cos ( 2 h cos y cosh t ) Ce 2 n ( t , h 2 ) d t = ( - 1 ) n + 1 1 2 π Mc 2 n ( 2 ) ( 0 , h ) ce 2 n ( y , h 2 ) , superscript subscript 0 2 𝑦 𝑡 modified-Mathieu-Ce 2 𝑛 𝑡 superscript 2 𝑡 superscript 1 𝑛 1 1 2 𝜋 modified-Mathieu-Mc 2 2 𝑛 0 Mathieu-ce 2 𝑛 𝑦 superscript 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\cos\left(2h\cos y\cosh t\right)% \mathrm{Ce}_{2n}\left(t,h^{2}\right)\mathrm{d}t=(-1)^{n+1}\tfrac{1}{2}\pi{% \mathrm{Mc}^{(2)}_{2n}}\left(0,h\right)\mathrm{ce}_{2n}\left(y,h^{2}\right),}}
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    DLMF:28.28.E15
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    ce n ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S2.SS6.p1.m7acdec
    0 references