Maxima Function
GosperSum (F_k, k, a, b)
Returns the summmation of F_k from k = a to k = b
if F_k has a hypergeometric anti-difference.
Otherwise, GosperSum
returns nongosper_summable
.
Examples:
(%i1) load (zeilberger); (%o1) /usr/share/maxima/share/contrib/Zeilberger/zeilberger.mac (%i2) GosperSum ((-1)^k*k / (4*k^2 - 1), k, 1, n); Dependent equations eliminated: (1) 3 n + 1 (n + -) (- 1) 2 1 (%o2) - ------------------ - - 2 4 2 (4 (n + 1) - 1) (%i3) GosperSum (1 / (4*k^2 - 1), k, 1, n); 3 - n - - 2 1 (%o3) -------------- + - 2 2 4 (n + 1) - 1 (%i4) GosperSum (x^k, k, 1, n); n + 1 x x (%o4) ------ - ----- x - 1 x - 1 (%i5) GosperSum ((-1)^k*a! / (k!*(a - k)!), k, 1, n); n + 1 a! (n + 1) (- 1) a! (%o5) - ------------------------- - ---------- a (- n + a - 1)! (n + 1)! a (a - 1)! (%i6) GosperSum (k*k!, k, 1, n); Dependent equations eliminated: (1) (%o6) (n + 1)! - 1 (%i7) GosperSum ((k + 1)*k! / (k + 1)!, k, 1, n); (n + 1) (n + 2) (n + 1)! (%o7) ------------------------ - 1 (n + 2)! (%i8) GosperSum (1 / ((a - k)!*k!), k, 1, n); (%o8) nonGosper_summable