拉卡多项式维基百科,自由的 encyclopedia 拉卡多项式(Racah polynomials)是数学中以Guilio Racah命名的正交多项式,由下列广义超几何函数定义[1] p n ( x ( x + γ + δ + 1 ) ) = 4 F 3 [ − n n + α + β + 1 − x x + γ + δ + 1 α + 1 γ + 1 β + δ + 1 ; 1 ] . {\displaystyle p_{n}(x(x+\gamma +\delta +1))={}_{4}F_{3}\left[{\begin{matrix}-n&n+\alpha +\beta +1&-x&x+\gamma +\delta +1\\\alpha +1&\gamma +1&\beta +\delta +1\\\end{matrix}};1\right].} 拉卡多项式 拉卡多项式的前数条是 h y p e r g e o m ( [ − 1 , − x , 2 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 2 , − x , 3 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 3 , − x , 4 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 4 , − x , 5 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 5 , − x , 6 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 6 , − x , 7 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) . {\displaystyle {\begin{aligned}hypergeom([-1,-x,2+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-2,-x,3+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-3,-x,4+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-4,-x,5+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-5,-x,6+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-6,-x,7+a+b,x+c+d+1],[a+1,c+1,b+d+1],1).\end{aligned}}}
拉卡多项式(Racah polynomials)是数学中以Guilio Racah命名的正交多项式,由下列广义超几何函数定义[1] p n ( x ( x + γ + δ + 1 ) ) = 4 F 3 [ − n n + α + β + 1 − x x + γ + δ + 1 α + 1 γ + 1 β + δ + 1 ; 1 ] . {\displaystyle p_{n}(x(x+\gamma +\delta +1))={}_{4}F_{3}\left[{\begin{matrix}-n&n+\alpha +\beta +1&-x&x+\gamma +\delta +1\\\alpha +1&\gamma +1&\beta +\delta +1\\\end{matrix}};1\right].} 拉卡多项式 拉卡多项式的前数条是 h y p e r g e o m ( [ − 1 , − x , 2 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 2 , − x , 3 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 3 , − x , 4 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 4 , − x , 5 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 5 , − x , 6 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) h y p e r g e o m ( [ − 6 , − x , 7 + a + b , x + c + d + 1 ] , [ a + 1 , c + 1 , b + d + 1 ] , 1 ) . {\displaystyle {\begin{aligned}hypergeom([-1,-x,2+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-2,-x,3+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-3,-x,4+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-4,-x,5+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-5,-x,6+a+b,x+c+d+1],[a+1,c+1,b+d+1],1)\\hypergeom([-6,-x,7+a+b,x+c+d+1],[a+1,c+1,b+d+1],1).\end{aligned}}}