DLMF:28.26.E4 (Q8420)

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DLMF:28.26.E4
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    Statements

    Defining formula
    \MathieuFc ⁢ m ⁢ @ ⁢ z ⁢ h ∼ 1 + s 8 ⁢ h ⁢ cosh 2 ⁡ z + 1 2 11 ⁢ h 2 ⁢ ( s 4 + 86 ⁢ s 2 + 105 cosh 4 ⁡ z - s 4 + 22 ⁢ s 2 + 57 cosh 2 ⁡ z ) + 1 2 14 ⁢ h 3 ⁢ ( - s 5 + 14 ⁢ s 3 + 33 ⁢ s cosh 2 ⁡ z - 2 ⁢ s 5 + 124 ⁢ s 3 + 1122 ⁢ s cosh 4 ⁡ z + 3 ⁢ s 5 + 290 ⁢ s 3 + 1627 ⁢ s cosh 6 ⁡ z ) + ⋯ , asymptotic-expansion \MathieuFc 𝑚 @ 𝑧 ℎ 1 𝑠 8 ℎ 2 𝑧 1 superscript 2 11 superscript ℎ 2 superscript 𝑠 4 86 superscript 𝑠 2 105 4 𝑧 superscript 𝑠 4 22 superscript 𝑠 2 57 2 𝑧 1 superscript 2 14 superscript ℎ 3 superscript 𝑠 5 14 superscript 𝑠 3 33 𝑠 2 𝑧 2 superscript 𝑠 5 124 superscript 𝑠 3 1122 𝑠 4 𝑧 3 superscript 𝑠 5 290 superscript 𝑠 3 1627 𝑠 6 𝑧 ⋯ {\displaystyle{\displaystyle\MathieuFc{m}@{z}{h}\sim 1+\dfrac{s}{8h{\cosh^{2}}% z}+\dfrac{1}{2^{11}h^{2}}\left(\dfrac{s^{4}+86s^{2}+105}{{\cosh^{4}}z}-\dfrac{% s^{4}+22s^{2}+57}{{\cosh^{2}}z}\right)+\dfrac{1}{2^{14}h^{3}}\left(-\dfrac{s^{% 5}+14s^{3}+33s}{{\cosh^{2}}z}-\dfrac{2s^{5}+124s^{3}+1122s}{{\cosh^{4}}z}+% \dfrac{3s^{5}+290s^{3}+1627s}{{\cosh^{6}}z}\right)+\cdots,}}
    0 references
    DLMF id
    DLMF:28.26.E4
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2abdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1cdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1cdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1cdec
    0 references
     
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