DLMF:28.26.E5 (Q8421)

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DLMF:28.26.E5
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    Statements

    Defining formula
    \MathieuGc ⁢ m ⁢ @ ⁢ z ⁢ h ∼ sinh ⁡ z cosh 2 ⁡ z ⁢ ( s 2 + 3 2 5 ⁢ h + 1 2 9 ⁢ h 2 ⁢ ( s 3 + 3 ⁢ s + 4 ⁢ s 3 + 44 ⁢ s cosh 2 ⁡ z ) + 1 2 14 ⁢ h 3 ⁢ ( 5 ⁢ s 4 + 34 ⁢ s 2 + 9 - s 6 - 47 ⁢ s 4 + 667 ⁢ s 2 + 2835 12 ⁢ cosh 2 ⁡ z + s 6 + 505 ⁢ s 4 + 12139 ⁢ s 2 + 10395 12 ⁢ cosh 4 ⁡ z ) ) + ⋯ . asymptotic-expansion \MathieuGc 𝑚 @ 𝑧 ℎ 𝑧 2 𝑧 superscript 𝑠 2 3 superscript 2 5 ℎ 1 superscript 2 9 superscript ℎ 2 superscript 𝑠 3 3 𝑠 4 superscript 𝑠 3 44 𝑠 2 𝑧 1 superscript 2 14 superscript ℎ 3 5 superscript 𝑠 4 34 superscript 𝑠 2 9 superscript 𝑠 6 47 superscript 𝑠 4 667 superscript 𝑠 2 2835 12 2 𝑧 superscript 𝑠 6 505 superscript 𝑠 4 12139 superscript 𝑠 2 10395 12 4 𝑧 ⋯ {\displaystyle{\displaystyle\MathieuGc{m}@{z}{h}\sim\dfrac{\sinh z}{{\cosh^{2}% }z}\left(\dfrac{s^{2}+3}{2^{5}h}+\dfrac{1}{2^{9}h^{2}}\left(s^{3}+3s+\dfrac{4s% ^{3}+44s}{{\cosh^{2}}z}\right)+\dfrac{1}{2^{14}h^{3}}\left(5s^{4}+34s^{2}+9-% \dfrac{s^{6}-47s^{4}+667s^{2}+2835}{12{\cosh^{2}}z}+\dfrac{s^{6}+505s^{4}+1213% 9s^{2}+10395}{12{\cosh^{4}}z}\right)\right)+\cdots.}}
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    DLMF id
    DLMF:28.26.E5
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2acdec
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