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DLMF:30.1#Ex4 - MaRDI portal

DLMF:30.1#Ex4 (Q9510)

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DLMF:30.1#Ex4
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    Statements

    DLMF defining formula
    d d x ⁡ S m ⁢ n ( 1 ) ⁢ ( γ , x ) | x = 0 = ( - 1 ) m ⁢ d d x ⁡ 𝖯 n m ⁡ ( x ) | x = 0 , evaluated-at derivative 𝑥 subscript superscript 𝑆 1 𝑚 𝑛 𝛾 𝑥 𝑥 0 evaluated-at superscript 1 𝑚 derivative 𝑥 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 𝑥 0 {\displaystyle{\displaystyle\left.\frac{\mathrm{d}}{\mathrm{d}x}S^{(1)}_{mn}(% \gamma,x)\right|_{x=0}=(-1)^{m}\left.\frac{\mathrm{d}}{\mathrm{d}x}\mathsf{P}^% {m}_{n}\left(x\right)\right|_{x=0},}}
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    constraint
    n - m 𝑛 𝑚 {\displaystyle{\displaystyle n-m}}
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    Identifiers

     
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