DLMF:28.28.E36 (Q8465): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12318 / rank
 
Normal rank
Property / Symbols used: Q12318 / qualifier
 
Defining formula:

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

\radMathieuDs{\NVar{j}}@{\NVar{n}}{\NVar{m}}{\NVar{z}}
Property / Symbols used: Q12318 / qualifier
 
xml-id: C28.S28.E35.m1aadec

Revision as of 15:28, 2 January 2020

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DLMF:28.28.E36
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    Defining formula
    sinh ⁡ z π 2 ⁢ ∫ 0 2 ⁢ π cos ⁡ t ⁢ se n ⁡ ( t , h 2 ) ⁢ se m ⁡ ( t , h 2 ) sinh 2 ⁡ z + sin 2 ⁡ t ⁢ d t = ( - 1 ) p + 1 ⁢ i ⁢ h ⁢ α ^ n , m ( s ) ⁢ Ds 0 ⁡ ( n , m , z ) , 𝑧 superscript 𝜋 2 superscript subscript 0 2 𝜋 𝑡 Mathieu-se 𝑛 𝑡 superscript ℎ 2 Mathieu-se 𝑚 𝑡 superscript ℎ 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 1 imaginary-unit ℎ superscript subscript ^ 𝛼 𝑛 𝑚 𝑠 Mathieu-Ds 0 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{se}_{m}\left(t,h^{2}\right)}{{\sinh% ^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p+1}\mathrm{i}h\widehat{\alpha}_{n,m}^{(s% )}\mathrm{Ds}_{0}\left(n,m,z\right),}}
    0 references
    DLMF id
    DLMF:28.28.E36
    0 references
    Symbols used
    Q12318
    Defining formula
    Ds j ⁡ ( n , m , z ) Mathieu-Ds 𝑗 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{Ds}_{\NVar{j}}\left(\NVar{n},\NVar{m},% \NVar{z}\right)}}
    xml-id
    C28.S28.E35.m1aadec
    0 references
     
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