<<SumCracker.m

SumCracker  Package by Manuel Kauers — © RISC Linz — V 0.11  2009-04-05

ZeroSequenceQ[ChebyshevT[n+2,x]-x ChebyshevT[n+1,x]+(1-x^2) ChebyshevU[n,x]]

(* Giving more information on the ongoing calculations *)

ZeroSequenceQ[ChebyshevT[n+2,x]-x ChebyshevT[n+1,x]+(1-x^2) ChebyshevU[n,x],Infolevel->2]

ApproximateAnnihilator[{Fibonacci[n],Fibonacci[n+1],(-1)^n}]

(* computing a linear recurrence for the given sequence *)

GetLinearRecurrence[HermiteH[2n,x],In->n,Head->h]

GetLinearRecurrence[SUM[(2k-1) JacobiP[k,1,0,x],{k,0,n}],In->n,Head->s]

(* default value for the output sequence is "SUM" (if no Head is specified) *)

GetLinearRecurrence[SUM[(2k-1) JacobiP[k,1,0,x],{k,0,n}],In->n]

(* finding closed form representations (if possible) *)

Crack[SUM[(2k+1) LegendreP[k,x],{k,0,2n}]]

(* finding closed form representations in terms of some given sequences (if possible) *)

Crack[SUM[(2k+1) LegendreP[k,x],{k,0,2n}],Into->{JacobiP[2n,1,0,x],n}]