chapter  6
Gosper’s Algorithm
Pages 6

With the quotient given in this form, we write the candidate for a solution to the sum (6.1) as

T (a, k) = h(k)s(k)t(a, k)

f(k) , (6.6)

where s(k) is an unknown function which we attempt to find. If the function defined by (6.6) solves equation (6.1), then using equa-

tion (6.5) we must have

t(a, k) = ∆T (a, k)

= h(k + 1)s(k + 1)t(a, k + 1)

f(k + 1) − h(k)s(k)t(a, k)

f(k)

= s(k + 1)t(a, k)g(k)

f(k) − h(k)s(k)t(a, k)

f(k)

= t(a, k) s(k + 1)g(k)− h(k)s(k)

f(k) .