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oct
oct
Commits
1d404aca
Commit
1d404aca
authored
Apr 06, 2012
by
Raymond Toy
Browse files
Add some comments, rename besseljexparc to integerbesseljexparc.
parent
4c1ed0f4
Changes
1
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qdbessel.lisp
View file @
1d404aca
...
...
@@ 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)) + (k1/2)*B[k1](p)/(2*p)
;;
;; The paper is missing the division by p in the term containing
;; B[k1](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
;; doublefloat 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
besseljexparc
(
v
z
)
(
defun
integer
besseljexparc
(
v
z
)
(
let*
((
iz
(
*
#c
(
0
1
)
z
))
(
i+
(
exparci2
iz
v
))
(
i
(
exparci2
(

iz
)
v
)))
...
...
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