DLMF:28.22.E4 (Q8369): 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
 
(10 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12286 / rank
 
Normal rank
Property / Symbols used: Q12286 / qualifier
 
Defining formula:

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

\Mathieuse{\NVar{n}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q12286 / qualifier
 
xml-id: C28.S2.SS6.p1.m8aadec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: modified Mathieu function / rank
 
Normal rank
Property / Symbols used: modified Mathieu function / qualifier
 
Defining formula:

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

\modMathieuGe{\NVar{n}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: modified Mathieu function / qualifier
 
xml-id: C28.S20.E7.m2adec
Property / Symbols used
 
Property / Symbols used: radial Mathieu function / rank
 
Normal rank
Property / Symbols used: radial Mathieu function / qualifier
 
Defining formula:

Ms n ( j ) ⁡ ( z , h ) modified-Mathieu-Ms 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}

\radMathieuMs{\NVar{j}}{\NVar{n}}@{\NVar{z}}{\NVar{h}}
Property / Symbols used: radial Mathieu function / qualifier
 
xml-id: C28.S20.E16.m2aadec
Property / Symbols used
 
Property / Symbols used: modified Mathieu function / rank
 
Normal rank
Property / Symbols used: modified Mathieu function / qualifier
 
Defining formula:

Se ν ⁡ ( z , q ) modified-Mathieu-Se 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Se}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}% \right)}}

\modMathieuSe{\NVar{\nu}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: modified Mathieu function / qualifier
 
xml-id: C28.S20.E4.m2aadec
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.m1cdec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12272 / rank
 
Normal rank
Property / Symbols used: Q12272 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12272 / qualifier
 
xml-id: C28.S1.XMD6.m1cdec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12303 / rank
 
Normal rank
Property / Symbols used: Q12303 / qualifier
 
Defining formula:

f e , n ⁢ ( h ) subscript 𝑓 𝑒 𝑛 ℎ {\displaystyle{\displaystyle f_{\mathit{e},n}(h)}}

f_{\mathit{e},n}(h)
Property / Symbols used: Q12303 / qualifier
 
xml-id: C28.S22.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q12290 / rank
 
Normal rank
Property / Symbols used: Q12290 / qualifier
 
Defining formula:

S n ⁢ ( q ) subscript 𝑆 𝑛 𝑞 {\displaystyle{\displaystyle S_{n}(q)}}

S_{n}(q)
Property / Symbols used: Q12290 / qualifier
 
xml-id: C28.S5.XMD4.m1dec

Latest revision as of 15:04, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.22.E4
No description defined

    Statements

    Defining formula
    Ms m ( 2 ) ⁡ ( z , h ) = 2 π ⁢ 1 g o , m ⁢ ( h ) ⁢ se m ′ ⁡ ( 0 , h 2 ) ⁢ ( - f o , m ⁢ ( h ) ⁢ Se m ⁡ ( z , h 2 ) - 2 π ⁢ S m ⁢ ( h 2 ) ⁢ Ge m ⁡ ( z , h 2 ) ) . modified-Mathieu-Ms 2 𝑚 𝑧 ℎ 2 𝜋 1 subscript 𝑔 𝑜 𝑚 ℎ diffop Mathieu-se 𝑚 1 0 superscript ℎ 2 subscript 𝑓 𝑜 𝑚 ℎ modified-Mathieu-Se 𝑚 𝑧 superscript ℎ 2 2 𝜋 subscript 𝑆 𝑚 superscript ℎ 2 modified-Mathieu-Ge 𝑚 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle{\mathrm{Ms}^{(2)}_{m}}\left(z,h\right)=\sqrt{% \frac{2}{\pi}}\dfrac{1}{g_{\mathit{o},m}(h)\mathrm{se}_{m}'\left(0,h^{2}\right% )}\*\left(-f_{\mathit{o},m}(h)\mathrm{Se}_{m}\left(z,h^{2}\right)-\dfrac{2}{% \pi S_{m}(h^{2})}\mathrm{Ge}_{m}\left(z,h^{2}\right)\right).}}
    0 references
    DLMF id
    DLMF:28.22.E4
    0 references
    Symbols used
    Q12286
    Defining formula
    se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m8aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    modified Mathieu function
    Defining formula
    Ge n ⁡ ( z , q ) modified-Mathieu-Ge 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E7.m2adec
    0 references
    radial Mathieu function
    Defining formula
    Ms n ( j ) ⁡ ( z , h ) modified-Mathieu-Ms 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E16.m2aadec
    0 references
    modified Mathieu function
    Defining formula
    Se ν ⁡ ( z , q ) modified-Mathieu-Se 𝜈 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{Se}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S20.E4.m2aadec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1cdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1cdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1cdec
    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.m1cdec
    0 references
    Q12303
    Defining formula
    f e , n ⁢ ( h ) subscript 𝑓 𝑒 𝑛 ℎ {\displaystyle{\displaystyle f_{\mathit{e},n}(h)}}
    xml-id
    C28.S22.XMD2.m1adec
    0 references
    Q12290
    Defining formula
    S n ⁢ ( q ) subscript 𝑆 𝑛 𝑞 {\displaystyle{\displaystyle S_{n}(q)}}
    xml-id
    C28.S5.XMD4.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8369&oldid=53937"