Definition:normJacobiR

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The LaTeX DLMF and DRMF macro \normJacobiR represents the normalized Jacobi polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\normJacobiR{\alpha}{\beta}{n} produces R n ( Ξ± , Ξ² ) normalized-Jacobi-polynomial-R 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle R^{(\alpha,\beta)}_{n}}}}
\normJacobiR{\alpha}{\beta}{n}@{x} produces R n ( Ξ± , Ξ² ) ⁑ ( x ) normalized-Jacobi-polynomial-R 𝛼 𝛽 𝑛 π‘₯ {\displaystyle{\displaystyle{\displaystyle R^{(\alpha,\beta)}_{n}\left(x\right% )}}}

These are defined by R n ( Ξ± , Ξ² ) ⁑ ( x ) := P n ( Ξ± , Ξ² ) ⁑ ( x ) P n ( Ξ± , Ξ² ) ⁑ ( 1 ) , assign normalized-Jacobi-polynomial-R 𝛼 𝛽 𝑛 π‘₯ Jacobi-polynomial-P 𝛼 𝛽 𝑛 π‘₯ Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 {\displaystyle{\displaystyle{\displaystyle R^{(\alpha,\beta)}_{n}\left(x\right% ):=\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1% \right)},}}} where P n ( Ξ± , Ξ² ) ⁑ ( 1 ) = ( Ξ± + 1 ) n n ! . Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 Pochhammer-symbol 𝛼 1 𝑛 𝑛 {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(1\right% )=\frac{{\left(\alpha+1\right)_{n}}}{n!}.}}}

Symbols List

R n ( Ξ± , Ξ² ) subscript superscript 𝑅 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle R^{(\alpha,\beta)}_{n}}}}  : normalized Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:normJacobiR
P n ( Ξ± , Ξ² ) subscript superscript 𝑃 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
( a ) n subscript π‘Ž 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii


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