DLMF:28.6.E23 (Q8257): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12286 / rank
 
Normal rank
Property / Symbols used: Q12286 / qualifier
 
Defining formula:

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

\Mathieuse{\NVar{n}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q12286 / qualifier
 
xml-id: C28.S2.SS6.p1.m8adec

Revision as of 14:46, 2 January 2020

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DLMF:28.6.E23
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    Statements

    se 1 ( z , q ) = sin z - 1 8 q sin 3 z + 1 128 q 2 ( 2 3 sin 5 z + 2 sin 3 z - sin z ) - 1 1024 q 3 ( 1 9 sin 7 z + 8 9 sin 5 z - 1 3 sin 3 z - 2 sin z ) + , Mathieu-se 1 𝑧 𝑞 𝑧 1 8 𝑞 3 𝑧 1 128 superscript 𝑞 2 2 3 5 𝑧 2 3 𝑧 𝑧 1 1024 superscript 𝑞 3 1 9 7 𝑧 8 9 5 𝑧 1 3 3 𝑧 2 𝑧 {\displaystyle{\displaystyle\mathrm{se}_{1}\left(z,q\right)=\sin z-\tfrac{1}{8% }q\sin 3z+\tfrac{1}{128}q^{2}\left(\tfrac{2}{3}\sin 5z+2\sin 3z-\sin z\right)-% \tfrac{1}{1024}q^{3}\left(\tfrac{1}{9}\sin 7z+\tfrac{8}{9}\sin 5z-\tfrac{1}{3}% \sin 3z-2\sin z\right)+\cdots,}}
    0 references
    DLMF:28.6.E23
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    se n ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S2.SS6.p1.m8adec
    0 references