Definition:monicKrawtchouk

From DRMF
Jump to navigation Jump to search

The LaTeX DLMF and DRMF macro \monicKrawtchouk represents the monic Krawtchouk polynomial.

This macro is in the category of polynomials.

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

\monicKrawtchouk{n} produces K ^ n Krawtchouk-polynomial-monic-p 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}
\monicKrawtchouk{n}@{q^{-x}}{p}{N}{q} produces K ^ n ⁑ ( q - x ; p , N ) ⁒ q Krawtchouk-polynomial-monic-p 𝑛 superscript π‘ž π‘₯ 𝑝 𝑁 π‘ž {\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}\!\left(q^{-x};p,N% \right){q}}}}
\monicKrawtchouk{n}@@{q^{-x}}{p}{N}{q} produces K ^ n ⁑ ( q - x ) ⁒ q Krawtchouk-polynomial-monic-p 𝑛 superscript π‘ž π‘₯ 𝑝 𝑁 π‘ž {\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}\!\left(q^{-x}% \right){q}}}}

These are defined by K n ⁑ ( x ; p , N ) = : 1 ( - N ) n ⁒ p n K ^ n ⁑ ( x ; p , N ) . fragments Krawtchouk-polynomial-K 𝑛 π‘₯ 𝑝 𝑁 : 1 Pochhammer-symbol 𝑁 𝑛 superscript 𝑝 𝑛 Krawtchouk-polynomial-monic-p 𝑛 π‘₯ 𝑝 𝑁 . {\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(x;p,N\right)=:\frac{1}% {{\left(-N\right)_{n}}p^{n}}{\widehat{K}}_{n}\!\left(x;p,N\right).}}}

Symbols List

K ^ n subscript ^ 𝐾 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}  : monic Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:monicKrawtchouk
K n subscript 𝐾 𝑛 {\displaystyle{\displaystyle{\displaystyle K_{n}}}}  : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6
( 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:monicKrawtchouk&oldid=5858"