DLMF:28.11.E5 (Q8295): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q12284 / rank
 
Normal rank
Property / Symbols used: Q12284 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12284 / qualifier
 
xml-id: C28.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
test:

q = h 2 𝑞 superscript 2 {\displaystyle{\displaystyle q=h^{2}}}

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12279 / rank
 
Normal rank
Property / Symbols used: Q12279 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12279 / qualifier
 
xml-id: C28.S1.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12272 / rank
 
Normal rank
Property / Symbols used: Q12272 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12272 / qualifier
 
xml-id: C28.S1.XMD6.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12287 / rank
 
Normal rank
Property / Symbols used: Q12287 / qualifier
 
test:

A m ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}

A_{m}(q)
Property / Symbols used: Q12287 / qualifier
 
xml-id: C28.S4.XMD1.m1bdec

Latest revision as of 13:53, 2 January 2020

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DLMF:28.11.E5
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    Statements

    cos ( 2 m + 1 ) z = n = 0 A 2 m + 1 2 n + 1 ( q ) ce 2 n + 1 ( z , q ) , 2 𝑚 1 𝑧 superscript subscript 𝑛 0 superscript subscript 𝐴 2 𝑚 1 2 𝑛 1 𝑞 Mathieu-ce 2 𝑛 1 𝑧 𝑞 {\displaystyle{\displaystyle\cos(2m+1)z=\sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)% \mathrm{ce}_{2n+1}\left(z,q\right),}}
    0 references
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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.m7addec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C28.S1.XMD1.m1adec
    0 references
    q = h 2 𝑞 superscript 2 {\displaystyle{\displaystyle q=h^{2}}}
    C28.S1.XMD10.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C28.S1.XMD2.m1ddec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C28.S1.XMD6.m1cdec
    0 references
    A m ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    C28.S4.XMD1.m1bdec
    0 references