DLMF:28.28.E15 (Q8439): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12279 / rank
 
Normal rank
Property / Symbols used: Q12279 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12279 / qualifier
 
xml-id: C28.S1.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12313 / rank
 
Normal rank
Property / Symbols used: Q12313 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q12313 / qualifier
 
xml-id: C28.S1.XMD5.m1dec

Latest revision as of 15:21, 2 January 2020

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DLMF:28.28.E15
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    Statements

    Defining formula
    ∫ 0 ∞ cos ⁡ ( 2 ⁢ h ⁢ cos ⁡ y ⁢ cosh ⁡ t ) ⁢ Ce 2 ⁢ n ⁡ ( t , h 2 ) ⁢ d t = ( - 1 ) n + 1 ⁢ 1 2 ⁢ π ⁢ Mc 2 ⁢ n ( 2 ) ⁡ ( 0 , h ) ⁢ ce 2 ⁢ n ⁡ ( y , h 2 ) , superscript subscript 0 2 ℎ 𝑦 𝑡 modified-Mathieu-Ce 2 𝑛 𝑡 superscript ℎ 2 𝑡 superscript 1 𝑛 1 1 2 𝜋 modified-Mathieu-Mc 2 2 𝑛 0 ℎ Mathieu-ce 2 𝑛 𝑦 superscript ℎ 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\cos\left(2h\cos y\cosh t\right)% \mathrm{Ce}_{2n}\left(t,h^{2}\right)\mathrm{d}t=(-1)^{n+1}\tfrac{1}{2}\pi{% \mathrm{Mc}^{(2)}_{2n}}\left(0,h\right)\mathrm{ce}_{2n}\left(y,h^{2}\right),}}
    0 references
    DLMF id
    DLMF:28.28.E15
    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.m7acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    modified Mathieu function
    Defining formula
    Ce ν ⁡ ( z , q ) modified-Mathieu-Ce 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E3.m2aadec
    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.m2acdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1ldec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1ddec
    0 references
    Q12313
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C28.S1.XMD5.m1dec
    0 references
     
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