DLMF:30.4.E4 (Q8848): Difference between revisions

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‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12404 / rank
 
Normal rank
Property / Symbols used: Q12404 / qualifier
 
Defining formula:

γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}

\gamma^{2}
Property / Symbols used: Q12404 / qualifier
 
xml-id: C30.S2.XMD3.m1bdec

Latest revision as of 01:42, 2 January 2020

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DLMF:30.4.E4
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    Statements

    Defining formula
    𝖯𝗌 n m ⁡ ( x , γ 2 ) = ( 1 - x 2 ) 1 2 ⁢ m ⁢ ∑ k = 0 ∞ g k ⁢ x k , spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 superscript 1 superscript 𝑥 2 1 2 𝑚 superscript subscript 𝑘 0 subscript 𝑔 𝑘 superscript 𝑥 𝑘 {\displaystyle{\displaystyle\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)=(1-x^% {2})^{\frac{1}{2}m}\sum_{k=0}^{\infty}g_{k}x^{k},}}
    0 references
    DLMF id
    DLMF:30.4.E4
    0 references
    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
    0 references
    Symbols used
    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.m1acdec
    0 references
    Q12419
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C30.S1.XMD2.m1cdec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1cdec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1cdec
    0 references
    Q12404
    Defining formula
    γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}
    xml-id
    C30.S2.XMD3.m1bdec
    0 references
     
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