## Clenshaw Recurrence Formula

The downward Clenshaw recurrence formula evaluates a sum of products of indexed Coefficients by functions which obey a recurrence relation. If

and

where the s are known, then define

for and solve backwards to obtain and .

The upward Clenshaw recurrence formula is

for .

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Recurrence Relations and Clenshaw's Recurrence Formula.'' §5.5 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 172-178, 1992.

© 1996-9 Eric W. Weisstein
1999-05-26