DLMF:28.28.E45 (Q8476): Difference between revisions

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Property / Symbols used
 
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.m7akdec

Revision as of 15:32, 2 January 2020

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DLMF:28.28.E45
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    Statements

    Defining formula
    sinh ⁡ ( 2 ⁢ z ) π 2 ⁢ ∫ 0 2 ⁢ π se n ′ ⁡ ( t , h 2 ) ⁢ ce m ⁡ ( t , h 2 ) sinh 2 ⁡ z + sin 2 ⁡ t ⁢ d t = ( - 1 ) p + 1 ⁢ i ⁢ γ ^ n , m ⁢ Dsc 1 ⁡ ( n , m , z ) , 2 𝑧 superscript 𝜋 2 superscript subscript 0 2 𝜋 diffop Mathieu-se 𝑛 1 𝑡 superscript ℎ 2 Mathieu-ce 𝑚 𝑡 superscript ℎ 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 1 imaginary-unit subscript ^ 𝛾 𝑛 𝑚 Mathieu-Dsc 1 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\dfrac{\sinh\left(2z\right)}{\pi^{2}}\int_{0}^{2% \pi}\dfrac{\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+1}\mathrm{i}\widehat{% \gamma}_{n,m}\mathrm{Dsc}_{1}\left(n,m,z\right),}}
    0 references
    DLMF id
    DLMF:28.28.E45
    0 references
    Symbols used
    Q12319
    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)}}
    xml-id
    C28.S28.E40.m1aedec
    0 references
    Q12283
    Defining formula
    ce n ⁡ ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m7akdec
    0 references
     
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