Changeset d795ba


Ignore:
Timestamp:
04/12/12 03:15:47 (3 years ago)
Author:
Raymond Toy <toy.raymond@…>
Branches:
master
Children:
6ab522
Parents:
c0e12d
Message:

Add TODO list for bessel-j.

File:
1 edited

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  • qd-bessel.lisp

    rc0e12d rd795ba  
    376376          (format t " term = ~S~%" term)
    377377          (format t " sum  = ~S~%" sum))))))
    378  
     378
     379;; TODO:
     380;;  o For |z| <= 1 use the series.
     381;;  o Currently accuracy is not good for large z and half-integer
     382;;    order.
     383;;  o For real v and z, return a real number instead of complex.
     384;;  o Handle the case of Re(z) < 0. (The formulas are for Re(z) > 0:
     385;;    bessel_j(v,z*exp(m*%pi*%i)) = exp(m*v*%pi*%i)*bessel_j(v, z)
     386;;  o The paper suggests using
     387;;      bessel_i(v,z) = exp(-v*%pi*%i/2)*bessel_j(v, %i*z)
     388;;    when Im(z) >> Re(z)
     389;;
    379390(defun bessel-j (v z)
    380391  (let ((vv (ftruncate v)))
     
    383394           (integer-bessel-j-exp-arc v z))
    384395          (t
     396           ;; Need to fine-tune the value of big-n.
    385397           (let ((big-n 100)
    386398                 (vpi (* v (float-pi (realpart z)))))
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