DLMF:28.22.E6 (Q8371): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(5 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.m2aedec
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.m1edec
Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1edec
Property / Symbols used
 
Property / Symbols used: Q12302 / rank
 
Normal rank
Property / Symbols used: Q12302 / qualifier
 
Defining formula:

g e , n ⁢ ( h ) subscript 𝑔 𝑒 𝑛 ℎ {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}

g_{\mathit{e},n}(h)
Property / Symbols used: Q12302 / qualifier
 
xml-id: C28.S22.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q12287 / rank
 
Normal rank
Property / Symbols used: Q12287 / qualifier
 
Defining formula:

A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}

A_{m}(q)
Property / Symbols used: Q12287 / qualifier
 
xml-id: C28.S4.XMD1.m1adec

Latest revision as of 15:04, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.22.E6
No description defined

    Statements

    Defining formula
    g e , 2 ⁢ m + 1 ⁢ ( h ) = ( - 1 ) m + 1 ⁢ 2 π ⁢ ce 2 ⁢ m + 1 ′ ⁡ ( 1 2 ⁢ π , h 2 ) h ⁢ A 1 2 ⁢ m + 1 ⁢ ( h 2 ) , subscript 𝑔 𝑒 2 𝑚 1 ℎ superscript 1 𝑚 1 2 𝜋 diffop Mathieu-ce 2 𝑚 1 1 1 2 𝜋 superscript ℎ 2 ℎ superscript subscript 𝐴 1 2 𝑚 1 superscript ℎ 2 {\displaystyle{\displaystyle g_{\mathit{e},2m+1}(h)=(-1)^{m+1}\sqrt{\frac{2}{% \pi}}\dfrac{\mathrm{ce}_{2m+1}'\left(\frac{1}{2}\pi,h^{2}\right)}{hA_{1}^{2m+1% }(h^{2})},}}
    0 references
    DLMF id
    DLMF:28.22.E6
    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.m2aedec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1edec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1edec
    0 references
    Q12302
    Defining formula
    g e , n ⁢ ( h ) subscript 𝑔 𝑒 𝑛 ℎ {\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}
    xml-id
    C28.S22.XMD1.m1edec
    0 references
    Q12287
    Defining formula
    A m ⁢ ( q ) subscript 𝐴 𝑚 𝑞 {\displaystyle{\displaystyle A_{m}(q)}}
    xml-id
    C28.S4.XMD1.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8371&oldid=54006"