On Fri, 31 Jan 2003 02:29:06 GMT, [EMAIL PROTECTED] (John) wrote: >I have a mathematical expression >(x-1)(x-2)+(x-1)(2x-3)+(x-1)(3x-4)+(2x-2)(2x-3)+(2x-2)(3x-4)+(3x-3)(3x-4) >It looks like it has some �rhythms� on the coefficient of x and on the >numbers subtracted from x. >Does the expression belong to some special polynomials or series?
It depends on what you mean by special. You could invent a sequence where f(x,1)=(x-1)(x-2) f(x,2)=(x-1)(x-2)+(x-1)(2x-3)+(2x-2)(2x-3) f(x,3)=(x-1)(x-2)+(x-1)(2x-3)+(x-1)(3x-4)+(2x-2)(2x-3)+(2x-2)(3x-4)+(3x-3)(3x-4) etc. and then work out that f(x,n)=(n+2)*(n+1)*n*(x-1)*((3n+1)*x-(3n+5))/24. And if you found this useful than it would be special for you. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
