Commit 1d404aca by Raymond Toy

### Add some comments, rename bessel-j-exp-arc to integer-bessel-j-exp-arc.

parent 4c1ed0f4
 ... ... @@ -51,6 +51,22 @@ ;; B[k](p) = 1/2^(k+3/2)/p^(k+1/2)*p^(k+1/2)*exp(-p)/CF ;; = exp(-p)/2^(k+3/2)/CF ;; ;; ;; Note also that [2] gives a recurrence relationship for B[k](p) in ;; eq (2.6), but there is an error there. The correct relationship is ;; ;; B[k](p) = -exp(-p)/(p*sqrt(2)*2^(k+1)) + (k-1/2)*B[k-1](p)/(2*p) ;; ;; The paper is missing the division by p in the term containing ;; B[k-1](p). This is easily derived from the recurrence relationship ;; for the (lower) incomplete gamma function. ;; ;; Note too that as k increases, the recurrence appears to be unstable ;; and B[k](p) begins to increase even though it is strictly bounded. ;; (This is also easy to see from the integral.) Hence, we do not use ;; the recursion. However, it might be stable for use with ;; double-float precision; this has not been tested. ;; (defun bk (k p) (/ (exp (- p)) (* (sqrt (float 2 (realpart p))) (ash 1 (+ k 1))) ... ... @@ -157,7 +173,7 @@ ;; This currently only works for v an integer. ;; (defun bessel-j-exp-arc (v z) (defun integer-bessel-j-exp-arc (v z) (let* ((iz (* #c(0 1) z)) (i+ (exp-arc-i-2 iz v)) (i- (exp-arc-i-2 (- iz ) v))) ... ...
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