DLMF:28.28.E4 (Q8425): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec

Revision as of 15:17, 2 January 2020

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DLMF:28.28.E4
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    Statements

    Defining formula
    i ⁢ h π ⁢ ∫ 0 2 ⁢ π ∂ ⁡ w ∂ ⁡ α ⁢ e 2 ⁢ i ⁢ h ⁢ w ⁢ ce n ⁡ ( t , h 2 ) ⁢ d t = i n ⁢ ce n ′ ⁡ ( α , h 2 ) ⁢ Mc 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-ce 𝑛 𝑡 superscript ℎ 2 𝑡 imaginary-unit 𝑛 diffop Mathieu-ce 𝑛 1 𝛼 superscript ℎ 2 modified-Mathieu-Mc 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{ce}_{n}\left(t,h^{2}\right% )\mathrm{d}t={\mathrm{i}^{n}}\mathrm{ce}_{n}'\left(\alpha,h^{2}\right){\mathrm% {Mc}^{(1)}_{n}}\left(z,h\right),}}
    0 references
    DLMF id
    DLMF:28.28.E4
    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.m7aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
     
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