DLMF:28.2.E31 (Q8177): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(7 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12283 / rank
 
Normal rank
Property / Symbols used: Q12283 / qualifier
 
Defining formula:

ce n ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

\Mathieuce{\NVar{n}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q12283 / qualifier
 
xml-id: C28.S2.SS6.p1.m7acdec
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.m2aqdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
Defining formula:

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

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1ydec
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.m1odec
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

Latest revision as of 14:36, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.2.E31
No description defined

    Statements

    0 2 π ce m ( x , q ) ce n ( x , q ) d x = 0 , superscript subscript 0 2 𝜋 Mathieu-ce 𝑚 𝑥 𝑞 Mathieu-ce 𝑛 𝑥 𝑞 𝑥 0 {\displaystyle{\displaystyle\int_{0}^{2\pi}\mathrm{ce}_{m}\left(x,q\right)% \mathrm{ce}_{n}\left(x,q\right)\mathrm{d}x=0,}}
    0 references
    DLMF:28.2.E31
    0 references
    n m 𝑛 𝑚 {\displaystyle{\displaystyle n\neq m}}
    0 references
    ce n ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    C28.S2.SS6.p1.m7acdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aqdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aadec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C28.S1.XMD1.m1dec
    0 references
    q = h 2 𝑞 superscript 2 {\displaystyle{\displaystyle q=h^{2}}}
    C28.S1.XMD10.m1ydec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C28.S1.XMD2.m1odec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C28.S1.XMD4.m1adec
    0 references