DLMF:28.12.E7 (Q8304): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aadec
Property / Symbols used
 
Property / Symbols used: Q12284 / rank
 
Normal rank
Property / Symbols used: Q12284 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12284 / qualifier
 
xml-id: C28.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
Defining formula:

q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1ddec
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.m1adec
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.m1adec
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.m1edec

Latest revision as of 14:55, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.12.E7
No description defined

    Statements

    Defining formula
    ∫ 0 π me ν + 2 ⁢ m ⁡ ( x , q ) ⁢ me ν + 2 ⁢ n ⁡ ( - x , q ) ⁢ d x = 0 , superscript subscript 0 𝜋 Mathieu-me 𝜈 2 𝑚 𝑥 𝑞 Mathieu-me 𝜈 2 𝑛 𝑥 𝑞 𝑥 0 {\displaystyle{\displaystyle{\int_{0}^{\pi}\mathrm{me}_{\nu+2m}\left(x,q\right% )\mathrm{me}_{\nu+2n}\left(-x,q\right)\mathrm{d}x=0,}}}
    0 references
    DLMF id
    DLMF:28.12.E7
    0 references
    constraint
    m ≠ n 𝑚 𝑛 {\displaystyle{\displaystyle m\neq n}}
    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1adec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1ddec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1adec
    0 references
    Q12285
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C28.S1.XMD4.m1adec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1edec
    0 references
     
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