DLMF:28.28.E20 (Q8446): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2apdec

Revision as of 15:22, 2 January 2020

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DLMF:28.28.E20
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    Statements

    Defining formula
    2 π ⁢ ∫ 0 π 𝒞 2 ⁢ ℓ ( j ) ⁢ ( 2 ⁢ h ⁢ R ) ⁢ cos ⁡ ( 2 ⁢ ℓ ⁢ ϕ ) ⁢ ce 2 ⁢ m ⁡ ( t , h 2 ) ⁢ d t = ε ℓ ⁢ ( - 1 ) ℓ + m ⁢ A 2 ⁢ ℓ 2 ⁢ m ⁢ ( h 2 ) ⁢ Mc 2 ⁢ m ( j ) ⁡ ( z , h ) , 2 𝜋 superscript subscript 0 𝜋 subscript superscript 𝒞 𝑗 2 ℓ 2 ℎ 𝑅 2 ℓ italic-ϕ Mathieu-ce 2 𝑚 𝑡 superscript ℎ 2 𝑡 subscript 𝜀 ℓ superscript 1 ℓ 𝑚 subscript superscript 𝐴 2 𝑚 2 ℓ superscript ℎ 2 modified-Mathieu-Mc 𝑗 2 𝑚 𝑧 ℎ {\displaystyle{\displaystyle\dfrac{2}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{2% \ell}(2hR)\cos\left(2\ell\phi\right)\mathrm{ce}_{2m}\left(t,h^{2}\right)% \mathrm{d}t=\varepsilon_{\ell}(-1)^{\ell+m}A^{2m}_{2\ell}(h^{2}){\mathrm{Mc}^{% (j)}_{2m}}\left(z,h\right),}}
    0 references
    DLMF id
    DLMF:28.28.E20
    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.m7aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
    0 references
     
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