Evaluation of the hypergeometric function using Gosper's method
Evaluation of the hypergeometric function using Gosper's method
hypergeo_gosper(A, B, C, z, tol = 0, maxiter = 2000)
A,B,C |
Parameters (real or complex) |
z |
Complex argument |
tol |
tolerance (passed to |
maxiter |
maximum number of iterations |
Gosper provides a three-term recurrence which converges when z is close to a critical point.
Bill Gosper asserts that the recursion holds for values of z which
are inside the cardioid (sqrt(8)*cos(t)-2*cos(2t),
sqrt(8)*sin(t)-2*sin(2t)) (see examples section).
It is suggested that the recursion should only be used when the auxiliary parameters A, B,C are all <=12 in absolute value.
R code by Robin K. S. Hankin, transcribed from maxima code posted by Richard Fateman, who credited Bill Gosper
Original email was archived at
https://www.ma.utexas.edu/pipermail/maxima/2006/000126.html but
does not appear there now; and the wayback machine doesn't find it
either.
hypergeo_gosper(1.1,5.1,3.1,crit()) # Compare MMA: -0.192225 + 0.692328 I t <- seq(from=0,to=2i*pi,len=100) plot(exp(t)*(sqrt(8)-exp(t)),asp=1,type='l') points(crit())
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