翻訳と辞書 Words near each other ・ Jack Frost (musician) ・ Jack Frost (politician) ・ Jack Frost (TV special) ・ Jack Frost Ski Resort ・ Jack Frusciante Has Left the Band ・ Jack Frusciante Left the Band ・ Jack Frye ・ Jack Fryer ・ Jack Fryer (footballer, born 1877) ・ Jack Fryer (footballer, born 1911) ・ Jack Fujimoto ・ Jack Fulbeck ・ Jack Fulk ・ Jack Fuller ・ Jack Fultz ・ Jack function ・ Jack Furness ・ Jack Furniss ・ Jack G. Downing ・ Jack G. Hanson ・ Jack G. Hills ・ Jack G. Merrell ・ Jack Gaffney ・ Jack Gage (director) ・ Jack Galbraith ・ Jack Gale ・ Jack Gallagher ・ Jack Gallagher (comedian) ・ Jack Gallagher (composer) ・ Jack Gallagher (wrestler) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Jack function ： ウィキペディア英語版 Jack function In mathematics, the Jack function, introduced by Henry Jack, is a homogeneous, symmetric polynomial which generalizes the Schur and zonal polynomials, and is in turn generalized by the Heckman–Opdam polynomials and Macdonald polynomials. ==Definition== The Jack function $J\_\backslash kappa^(x\_1,x\_2,\backslash ldots,x\_m)$ of integer partition $\backslash kappa$, parameter $\backslash alpha$ and arguments $x\_1,x\_2,\backslash ldots,$ can be recursively defined as follows: ; For ''m''=1 : : $J\_^(x\_1)=x\_1^k(1+\backslash alpha)\backslash cdots\; (1+(k-1)\backslash alpha)$ ; For ''m''>1: : $J\_\backslash kappa^(x\_1,x\_2,\backslash ldots,x\_m)=\backslash sum\_\backslash mu$ J_\mu^(x_1,x_2,\ldots,x_) x_m^\beta_, where the summation is over all partitions $\backslash mu$ such that the skew partition $\backslash kappa/\backslash mu$ is a horizontal strip, namely :$$ \kappa_1\ge\mu_1\ge\kappa_2\ge\mu_2\ge\cdots\ge\kappa_\ge\mu_\ge\kappa_n ($\backslash mu\_n$ must be zero or otherwise $J\_\backslash mu(x\_1,\backslash ldots,x\_)=0$) and :$$ \beta_=\frac^\kappa(i,j) }^\mu(i,j) }, where $B\_^\backslash nu(i,j)$ equals $\backslash kappa\_j\text{'}-i+\backslash alpha(\backslash kappa\_i-j+1)$ if $\backslash kappa\_j\text{'}=\backslash mu\_j\text{'}$ and $\backslash kappa\_j\text{'}-i+1+\backslash alpha(\backslash kappa\_i-j)$ otherwise. The expressions $\backslash kappa\text{'}$ and $\backslash mu\text{'}$ refer to the conjugate partitions of $\backslash kappa$ and $\backslash mu$, respectively. The notation $(i,j)\backslash in\backslash kappa$ means that the product is taken over all coordinates $(i,j)$ of boxes in the Young diagram of the partition $\backslash kappa$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jack function」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.