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DLMF:28.31.E17 - MaRDI portal

DLMF:28.31.E17 (Q9231)

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DLMF:28.31.E17
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    Statements

    DLMF defining formula
    β„Žπ‘  p m ⁒ ( z , ΞΎ ) = e - 1 4 ⁒ ΞΎ ⁒ cos ⁑ ( 2 ⁒ z ) ⁒ S p m ⁒ ( z , ΞΎ ) , superscript subscript β„Žπ‘  𝑝 π‘š 𝑧 πœ‰ superscript 𝑒 1 4 πœ‰ 2 𝑧 superscript subscript 𝑆 𝑝 π‘š 𝑧 πœ‰ {\displaystyle{\displaystyle\mathit{hs}_{p}^{m}(z,\xi)=e^{-\frac{1}{4}\xi\cos% \left(2z\right)}S_{p}^{m}(z,\xi),}}
    0 references
    Symbols used
    cosine function
    DLMF defining formula
    cos ⁑ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2afdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    integer
    DLMF defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1gdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1hdec
    0 references
    Ince polynomials (locally)
    DLMF defining formula
    S p m ⁒ ( z , N ⁒ V ⁒ a ⁒ r ⁒ x ⁒ i ) superscript subscript 𝑆 𝑝 π‘š 𝑧 𝑁 𝑉 π‘Ž π‘Ÿ π‘₯ 𝑖 {\displaystyle{\displaystyle S_{\NVar{p}}^{\NVar{m}}(\NVar{z},\\ NVar{xi})}}
    xml-id
    C28.S31.XMD7.m1ddec
    0 references

    Identifiers

     
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