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- Log ----------------------------------------------------------------- commit f203389e5e78d1f001f68447ac2a9dd86dcfbbf6 Author: Raymond Toy toy.raymond@gmail.com Date: Tue Apr 10 00:45:13 2012 -0700

* Implement sum-big-ia. * Add series for Bessel J. (Not working yet.)

diff --git a/qd-bessel.lisp b/qd-bessel.lisp index fbe9760..9759044 100644 --- a/qd-bessel.lisp +++ b/qd-bessel.lisp @@ -324,8 +324,41 @@ (incomplete-gamma-tail a (* theta z)))))

(defun sum-big-ia (big-n v z) - ) + (let ((big-n-1/2 (+ big-n 1/2)) + (eps (epsilon z))) + (do* ((n 0 (1+ n)) + (term (* (big-a 0 v) + (big-i 0 big-n-1/2 z v)) + (* (big-a n v) + (big-i n big-n-1/2 z v))) + (sum term (+ sum term))) + ((<= (abs term) (* eps (abs sum))) + sum) + #+nil + (progn + (format t "n = ~D~%" n) + (format t " term = ~S~%" term) + (format t " sum = ~S~%" sum)))))

+;; Series for bessel J: +;; +;; (z/2)^v*sum((-1)^k/Gamma(k+v+1)/k!*(z^2//4)^k, k, 0, inf) +(defun s-bessel-j (v z) + (with-floating-point-contagion (v z) + (let ((z2/4 (* z z 1/4)) + (eps (epsilon z))) + (do* ((k 0 (+ 1 k)) + (f (gamma (+ v 1)) + (* f (* k (+ v k)))) + (term (/ f) + (/ (* (- term) z2/4) f)) + (sum term (+ sum term))) + ((<= (abs term) (* eps (abs sum))) + (* sum (expt (* z 1/2) v))) + (format t "k = ~D~%" k) + (format t " term = ~S~%" term) + (format t " sum = ~S~%" sum))))) + (defun bessel-j (v z) (let ((vv (ftruncate v))) (cond ((= vv v) @@ -338,7 +371,8 @@ (* z (/ (sin vpi) vpi) (+ (/ -1 z) - (sum-ab big-n v z))))))))) + (sum-ab big-n v z) + (sum-big-ia big-n v z)))))))))  (defun paris-series (v z n) (labels ((pochhammer (a k)

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Summary of changes: qd-bessel.lisp | 38 ++++++++++++++++++++++++++++++++++++-- 1 files changed, 36 insertions(+), 2 deletions(-)

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