DLMF:28.28.E5 (Q8426): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12274 / rank
 
Normal rank
Property / Symbols used: Q12274 / qualifier
 
Defining formula:

w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}

w(z)
Property / Symbols used: Q12274 / qualifier
 
xml-id: C28.S2.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12311 / rank
 
Normal rank
Property / Symbols used: Q12311 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q12311 / qualifier
 
xml-id: C28.S28.XMD1.m1ddec

Latest revision as of 15:18, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:28.28.E5
No description defined

    Statements

    Defining formula
    i ⁢ h π ⁢ ∫ 0 2 ⁢ π ∂ ⁡ w ∂ ⁡ α ⁢ e 2 ⁢ i ⁢ h ⁢ w ⁢ se n ⁡ ( t , h 2 ) ⁢ d t = i n ⁢ se n ′ ⁡ ( α , h 2 ) ⁢ Ms n ( 1 ) ⁡ ( z , h ) . imaginary-unit ℎ 𝜋 superscript subscript 0 2 𝜋 partial-derivative 𝑤 𝛼 superscript 𝑒 2 imaginary-unit ℎ 𝑤 Mathieu-se 𝑛 𝑡 superscript ℎ 2 𝑡 imaginary-unit 𝑛 diffop Mathieu-se 𝑛 1 𝛼 superscript ℎ 2 modified-Mathieu-Ms 1 𝑛 𝑧 ℎ {\displaystyle{\displaystyle\dfrac{\mathrm{i}h}{\pi}\int_{0}^{2\pi}\frac{% \partial w}{\partial\alpha}e^{2\mathrm{i}hw}\mathrm{se}_{n}\left(t,h^{2}\right% )\mathrm{d}t={\mathrm{i}^{n}}\mathrm{se}_{n}'\left(\alpha,h^{2}\right){\mathrm% {Ms}^{(1)}_{n}}\left(z,h\right).}}
    0 references
    DLMF id
    DLMF:28.28.E5
    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
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    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
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4aadec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1cdec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1cdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1ddec
    0 references
    Q12274
    Defining formula
    w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}
    xml-id
    C28.S2.XMD1.m1ddec
    0 references
    Q12311
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C28.S28.XMD1.m1ddec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8426&oldid=56386"