Definition:monicJacobi

From DRMF
Jump to navigation Jump to search

The LaTeX DLMF and DRMF macro \monicJacobi represents the monic Jacobi polynomial.

This macro is in the category of polynomials.

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

\monicJacobi{n} produces P ^ missing ( n , ) ⁒ Jacobi-polynomial-monic-p 𝑛 absent absent absent {\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n,)}_{missing}{}}}}
\monicJacobi{n}@{x} produces P ^ x ( n , @ ) Jacobi-polynomial-monic-p 𝑛 @ π‘₯ {\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n,@)}_{x}}}}
\monicJacobi{n}@@{x} produces P ^ @ ( n , @ ) ⁒ x Jacobi-polynomial-monic-p 𝑛 @ @ π‘₯ {\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n,@)}_{@}{x}}}}

These are defined by P n ( Ξ± , Ξ² ) ⁑ ( x ) = : ( n + Ξ± + Ξ² + 1 ) n 2 n ⁒ n ! P ^ n ( Ξ± , Ξ² ) ⁑ ( x ) fragments Jacobi-polynomial-P 𝛼 𝛽 𝑛 π‘₯ : Pochhammer-symbol 𝑛 𝛼 𝛽 1 𝑛 superscript 2 𝑛 𝑛 Jacobi-polynomial-monic-p 𝛼 𝛽 𝑛 π‘₯ {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(x\right% )=:\frac{{\left(n+\alpha+\beta+1\right)_{n}}}{2^{n}n!}{\widehat{P}}^{(\alpha,% \beta)}_{n}\left(x\right)}}}

Symbols List

P ^ n ( Ξ± , Ξ² ) subscript superscript ^ 𝑃 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(\alpha,\beta)}_{n}}}}  : monic Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:monicJacobi
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


Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Definition:monicJacobi&oldid=5856"