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

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2acdec

Revision as of 15:17, 2 January 2020

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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
     
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