DLMF:28.26.E1 (Q8417)

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DLMF:28.26.E1
No description defined

    Statements

    Defining formula
    Mc m ( 3 ) ⁡ ( z , h ) = e i ⁢ ϕ ( π ⁢ h ⁢ cosh ⁡ z ) 1 / 2 ⁢ ( \MathieuFc ⁢ m ⁢ @ ⁢ z ⁢ h - i ⁢ \MathieuGc ⁢ m ⁢ @ ⁢ z ⁢ h ) , modified-Mathieu-Mc 3 𝑚 𝑧 ℎ superscript 𝑒 imaginary-unit italic-ϕ superscript 𝜋 ℎ 𝑧 1 2 \MathieuFc 𝑚 @ 𝑧 ℎ imaginary-unit \MathieuGc 𝑚 @ 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Mc}^{(3)}_{m}}\left(z,h\right)=\dfrac{e^{% \mathrm{i}\phi}}{(\pi h\cosh z)^{\ifrac{1}{2}}}\*\left(\MathieuFc{m}@{z}{h}-% \mathrm{i}\MathieuGc{m}@{z}{h}\right),}}
    0 references
    DLMF id
    DLMF:28.26.E1
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    radial Mathieu function
    Defining formula
    Mc n ( j ) ⁡ ( z , h ) modified-Mathieu-Mc 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E15.m2adec
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    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1dec
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    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1dec
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    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1dec
    0 references
    Q12310
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C28.S26.XMD1.m1dec
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