DLMF:28.28.E23 (Q8449): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12315 / rank
 
Normal rank
Property / Symbols used: Q12315 / qualifier
 
Defining formula:

R ⁢ ( z , t ) 𝑅 𝑧 𝑡 {\displaystyle{\displaystyle R(z,t)}}

R(z,t)
Property / Symbols used: Q12315 / qualifier
 
xml-id: C28.S28.XMD5.m1edec
Property / Symbols used
 
Property / Symbols used: Q12288 / rank
 
Normal rank
Property / Symbols used: Q12288 / qualifier
 
Defining formula:

B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}

B_{m}(q)
Property / Symbols used: Q12288 / qualifier
 
xml-id: C28.S4.XMD2.m1adec

Latest revision as of 15:24, 2 January 2020

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DLMF:28.28.E23
No description defined

    Statements

    Defining formula
    2 π ⁢ ∫ 0 π 𝒞 2 ⁢ ℓ + 2 ( j ) ⁢ ( 2 ⁢ h ⁢ R ) ⁢ sin ⁡ ( ( 2 ⁢ ℓ + 2 ) ⁢ ϕ ) ⁢ se 2 ⁢ m + 2 ⁡ ( t , h 2 ) ⁢ d t = ( - 1 ) ℓ + m ⁢ B 2 ⁢ ℓ + 2 2 ⁢ m + 2 ⁢ ( h 2 ) ⁢ Ms 2 ⁢ m + 2 ( j ) ⁡ ( z , h ) . 2 𝜋 superscript subscript 0 𝜋 subscript superscript 𝒞 𝑗 2 ℓ 2 2 ℎ 𝑅 2 ℓ 2 italic-ϕ Mathieu-se 2 𝑚 2 𝑡 superscript ℎ 2 𝑡 superscript 1 ℓ 𝑚 subscript superscript 𝐵 2 𝑚 2 2 ℓ 2 superscript ℎ 2 modified-Mathieu-Ms 𝑗 2 𝑚 2 𝑧 ℎ {\displaystyle{\displaystyle\dfrac{2}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{2% \ell+2}(2hR)\sin\left((2\ell+2)\phi\right)\mathrm{se}_{2m+2}\left(t,h^{2}% \right)\mathrm{d}t=(-1)^{\ell+m}B^{2m+2}_{2\ell+2}(h^{2}){\mathrm{Ms}^{(j)}_{2% m+2}}\left(z,h\right).}}
    0 references
    DLMF id
    DLMF:28.28.E23
    0 references
    Symbols used
    Q12286
    Defining formula
    se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m8addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2asdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aqdec
    0 references
    radial Mathieu function
    Defining formula
    Ms n ( j ) ⁡ ( z , h ) modified-Mathieu-Ms 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E16.m2addec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1edec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1rdec
    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.m1sdec
    0 references
    Q12304
    Defining formula
    𝒞 μ ( j ) superscript subscript 𝒞 𝜇 𝑗 {\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
    xml-id
    C28.S23.XMD1.m1ddec
    0 references
    Q12314
    Defining formula
    ϕ ⁢ ( z , t ) italic-ϕ 𝑧 𝑡 {\displaystyle{\displaystyle\phi(z,t)}}
    xml-id
    C28.S28.XMD4.m1edec
    0 references
    Q12315
    Defining formula
    R ⁢ ( z , t ) 𝑅 𝑧 𝑡 {\displaystyle{\displaystyle R(z,t)}}
    xml-id
    C28.S28.XMD5.m1edec
    0 references
    Q12288
    Defining formula
    B m ⁢ ( q ) subscript 𝐵 𝑚 𝑞 {\displaystyle{\displaystyle B_{m}(q)}}
    xml-id
    C28.S4.XMD2.m1adec
    0 references
     
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