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DLMF:18.9.E5

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Formula:6298
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MaRDI QIDQ6298

  • Label: DLMF:18.9.E5


Digital Library of Mathematical Functions ID 18.9.E5

( 2 ⁢ n + α + β + 1 ) ⁢ P n ( α , β ) ⁡ ( x ) = ( n + α + β + 1 ) ⁢ P n ( α , β + 1 ) ⁡ ( x ) + ( n + α ) ⁢ P n - 1 ( α , β + 1 ) ⁡ ( x ) , 2 𝑛 𝛼 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑛 𝛼 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 1 𝑛 𝑥 𝑛 𝛼 Jacobi-polynomial-P 𝛼 𝛽 1 𝑛 1 𝑥 {\displaystyle{\displaystyle(2n+\alpha+\beta+1)P^{(\alpha,\beta)}_{n}\left(x% \right)=(n+\alpha+\beta+1)P^{(\alpha,\beta+1)}_{n}\left(x\right)+(n+\alpha)P^{% (\alpha,\beta+1)}_{n-1}\left(x\right),}}


Constraint(s)

Symbols List

  • P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}} : Jacobi polynomial
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
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