DLMF:30.4.E9 (Q8853)

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DLMF:30.4.E9
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    Statements

    Defining formula
    lim N → ∞ ⁡ ∫ - 1 1 | f ⁢ ( x ) - ∑ n = m N c n ⁢ 𝖯𝗌 n m ⁡ ( x , γ 2 ) | 2 ⁢ d x = 0 . subscript → 𝑁 superscript subscript 1 1 𝑓 𝑥 superscript subscript 𝑛 𝑚 𝑁 subscript 𝑐 𝑛 spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 2 𝑥 0 {\displaystyle{\displaystyle\lim_{N\to\infty}\int_{-1}^{1}{\left|f(x)-\sum_{n=% m}^{N}c_{n}\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)\right|^{2}}\mathrm{d}x% =0.}}
    0 references
    DLMF id
    DLMF:30.4.E9
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q12418
    Defining formula
    𝖯𝗌 n m ⁡ ( x , γ 2 ) spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S4.SS1.m1agdec
    0 references
    Q12419
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C30.S1.XMD2.m1fdec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1hdec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1hdec
    0 references
    Q12404
    Defining formula
    γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}
    xml-id
    C30.S2.XMD3.m1gdec
    0 references
     
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