DLMF:28.23.E11 (Q8395): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m1jdec
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.m1idec
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.m1jdec
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 15:09, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.23.E11
No description defined

    Statements

    Defining formula
    Ms 2 ⁢ m + 1 ( j ) ⁡ ( z , h ) = ( - 1 ) m ⁢ ( se 2 ⁢ m + 1 ⁡ ( 1 2 ⁢ π , h 2 ) ) - 1 ⁢ ∑ ℓ = 0 ∞ B 2 ⁢ ℓ + 1 2 ⁢ m + 1 ⁢ ( h 2 ) ⁢ 𝒞 2 ⁢ ℓ + 1 ( j ) ⁢ ( 2 ⁢ h ⁢ sinh ⁡ z ) , modified-Mathieu-Ms 𝑗 2 𝑚 1 𝑧 ℎ superscript 1 𝑚 superscript Mathieu-se 2 𝑚 1 1 2 𝜋 superscript ℎ 2 1 superscript subscript ℓ 0 superscript subscript 𝐵 2 ℓ 1 2 𝑚 1 superscript ℎ 2 superscript subscript 𝒞 2 ℓ 1 𝑗 2 ℎ 𝑧 {\displaystyle{\displaystyle{\mathrm{Ms}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m% }\left(\mathrm{se}_{2m+1}\left(\tfrac{1}{2}\pi,h^{2}\right)\right)^{-1}\sum_{% \ell=0}^{\infty}B_{2\ell+1}^{2m+1}(h^{2}){\cal C}_{2\ell+1}^{(j)}(2h\sinh z),}}
    0 references
    DLMF id
    DLMF:28.23.E11
    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.m8aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2addec
    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.m2aadec
    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.m1idec
    0 references
    Q12291
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C28.S1.XMD3.m1jdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1idec
    0 references
    Q12304
    Defining formula
    𝒞 μ ( j ) superscript subscript 𝒞 𝜇 𝑗 {\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
    xml-id
    C28.S23.XMD1.m1jdec
    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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8395&oldid=54868"