DLMF:28.23.E8 (Q8392): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12284 / rank
 
Normal rank
Property / Symbols used: Q12284 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12284 / qualifier
 
xml-id: C28.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12291 / rank
 
Normal rank
Property / Symbols used: Q12291 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12291 / qualifier
 
xml-id: C28.S1.XMD3.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12272 / rank
 
Normal rank
Property / Symbols used: Q12272 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12272 / qualifier
 
xml-id: C28.S1.XMD6.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12304 / rank
 
Normal rank
Property / Symbols used: Q12304 / qualifier
 
Defining formula:

𝒞 μ ( j ) superscript subscript 𝒞 𝜇 𝑗 {\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}

\mathcal{C}_{\mu}^{(j)}
Property / Symbols used: Q12304 / qualifier
 
xml-id: C28.S23.XMD1.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12287 / rank
 
Normal rank
Property / Symbols used: Q12287 / qualifier
 
Defining formula:

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 15:08, 2 January 2020

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Language Label Description Also known as
English
DLMF:28.23.E8
No description defined

    Statements

    Defining formula
    Mc 2 ⁢ m + 1 ( j ) ⁡ ( z , h ) = ( - 1 ) m ⁢ ( ce 2 ⁢ m + 1 ⁡ ( 0 , h 2 ) ) - 1 ⁢ ∑ ℓ = 0 ∞ ( - 1 ) ℓ ⁢ A 2 ⁢ ℓ + 1 2 ⁢ m + 1 ⁢ ( h 2 ) ⁢ 𝒞 2 ⁢ ℓ + 1 ( j ) ⁢ ( 2 ⁢ h ⁢ cosh ⁡ z ) , modified-Mathieu-Mc 𝑗 2 𝑚 1 𝑧 ℎ superscript 1 𝑚 superscript Mathieu-ce 2 𝑚 1 0 superscript ℎ 2 1 superscript subscript ℓ 0 superscript 1 ℓ superscript subscript 𝐴 2 ℓ 1 2 𝑚 1 superscript ℎ 2 superscript subscript 𝒞 2 ℓ 1 𝑗 2 ℎ 𝑧 {\displaystyle{\displaystyle{\mathrm{Mc}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m% }\left(\mathrm{ce}_{2m+1}\left(0,h^{2}\right)\right)^{-1}\sum_{\ell=0}^{\infty% }(-1)^{\ell}A_{2\ell+1}^{2m+1}(h^{2}){\cal C}_{2\ell+1}^{(j)}(2h\cosh z),}}
    0 references
    DLMF id
    DLMF:28.23.E8
    0 references
    Symbols used
    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.m7abdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2acdec
    0 references
    radial Mathieu function
    Defining formula
    Mc n ( j ) ⁡ ( z , h ) modified-Mathieu-Mc 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E15.m2abdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1bdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1fdec
    0 references
    Q12291
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C28.S1.XMD3.m1gdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1fdec
    0 references
    Q12304
    Defining formula
    𝒞 μ ( j ) superscript subscript 𝒞 𝜇 𝑗 {\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
    xml-id
    C28.S23.XMD1.m1gdec
    0 references
    Q12287
    Defining formula
    A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    xml-id
    C28.S4.XMD1.m1bdec
    0 references
     
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