DLMF:28.12.E5 (Q8302): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12285 / rank
 
Normal rank
Property / Symbols used: Q12285 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12285 / qualifier
 
xml-id: C28.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12278 / rank
 
Normal rank
Property / Symbols used: Q12278 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12278 / qualifier
 
xml-id: C28.S1.XMD7.m1cdec

Latest revision as of 14:54, 2 January 2020

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DLMF:28.12.E5
No description defined

    Statements

    Defining formula
    ∫ 0 π me ν ⁡ ( x , q ) ⁢ me ν ⁡ ( - x , q ) ⁢ d x = π . superscript subscript 0 𝜋 Mathieu-me 𝜈 𝑥 𝑞 Mathieu-me 𝜈 𝑥 𝑞 𝑥 𝜋 {\displaystyle{\displaystyle\int_{0}^{\pi}\mathrm{me}_{\nu}\left(x,q\right)% \mathrm{me}_{\nu}\left(-x,q\right)\mathrm{d}x=\pi.}}
    0 references
    DLMF id
    DLMF:28.12.E5
    0 references
    Symbols used
    Q12299
    Defining formula
    me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S12.SS2.p2.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1bdec
    0 references
    Q12285
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C28.S1.XMD4.m1dec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1cdec
    0 references
     
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