DLMF:18.11.E1 (Q5635): Difference between revisions

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Property / constraint
 

0 ≤ m ≤ n 0 𝑚 𝑛 {\displaystyle{\displaystyle 0\leq m\leq n}}

0\leq m\leq n
Property / constraint: 0 ≤ m ≤ n 0 𝑚 𝑛 {\displaystyle{\displaystyle 0\leq m\leq n}} / rank
 
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Revision as of 16:59, 30 December 2019

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DLMF:18.11.E1
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    Statements

    test
    𝖯 n m ⁡ ( x ) = ( 1 2 ) m ⁢ ( - 2 ) m ⁢ ( 1 - x 2 ) 1 2 ⁢ m ⁢ C n - m ( m + 1 2 ) ⁡ ( x ) = ( n + 1 ) m ⁢ ( - 2 ) - m ⁢ ( 1 - x 2 ) 1 2 ⁢ m ⁢ P n - m ( m , m ) ⁡ ( x ) , Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 Pochhammer 1 2 𝑚 superscript 2 𝑚 superscript 1 superscript 𝑥 2 1 2 𝑚 ultraspherical-Gegenbauer-polynomial 𝑚 1 2 𝑛 𝑚 𝑥 Pochhammer 𝑛 1 𝑚 superscript 2 𝑚 superscript 1 superscript 𝑥 2 1 2 𝑚 Jacobi-polynomial-P 𝑚 𝑚 𝑛 𝑚 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(x\right)={\left(\tfrac{1}{% 2}\right)_{m}}(-2)^{m}(1-x^{2})^{\frac{1}{2}m}C^{(m+\frac{1}{2})}_{n-m}\left(x% \right)={\left(n+1\right)_{m}}(-2)^{-m}(1-x^{2})^{\frac{1}{2}m}P^{(m,m)}_{n-m}% \left(x\right),}}
    0 references
    DLMF id
    DLMF:18.11.E1
    0 references
    constraint
    0 ≤ m ≤ n 0 𝑚 𝑛 {\displaystyle{\displaystyle 0\leq m\leq n}}
    0 references
     
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