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From: SourceForge.net <noreply@so...>  20030525 15:01:40

Bugs item #736535, was opened at 20030512 12:21 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=736535&group_id=4933 Category: None Group: None >Status: Closed >Resolution: Fixed Priority: 5 Submitted By: Barton Willis (willisb) Assigned to: Raymond Toy (rtoy) Summary: half integer bessel_y function Initial Comment: The halfinteger bessel functions of the second kind (the Y functions) evaluate incorrectly. Consider (C1) besselexpand : true; (D1) TRUE (C2) w : bessel_y[1/2](x)$ (C3) display2d : false; (D3) FALSE (C4) ev(w); (D4) SQRT(2)*SIN(x)/(SQRT(%PI)*SQRT(x)) (C5) The sin(x) upstairs should be a cos(x); to fix this, I think we need to swap %sin and %cos in bessselysimp; change the line (simplify `((mtimes) 1 ,(besseljyhalforder arg rat order '%sin '%cos))) to (simplify `((mtimes) 1 ,(besseljyhalforder arg rat order '%cos '%sin))) Additionally, the halfinteger bessel functions evaluate to elementary functions too slowly. Consider (D5) ALL (C6) besselexpand : true; Evaluation took 0.00 seconds (0.00 elapsed) (D6) TRUE (C7) w : bessel_j[19/2](x)$ Evaluation took 0.82 seconds (0.82 elapsed) (C8) w : bessel_j[21/2](x)$ Evaluation took 2.47 seconds (2.47 elapsed) (C9) w : bessel_j[23/2](x)$ Evaluation took 43.87 seconds (43.87 elapsed) The time is increasing much too rapidly. Barton  >Comment By: Raymond Toy (rtoy) Date: 20030525 11:01 Message: Logged In: YES user_id=28849 Both of these issues should be fixed. The derivative with respect to order only done for J, though.  Comment By: Raymond Toy (rtoy) Date: 20030512 23:57 Message: Logged In: YES user_id=28849 The slow evaluation of the halfinteger functions is caused by a poor choice of algorithms. It computes a larger order derivative to find the answer. Should use a different algorithm such as the one in A&S 10.1.8 and 10.1.9.  Comment By: Raymond Toy (rtoy) Date: 20030512 23:54 Message: Logged In: YES user_id=28849 The slow evaluation of the halfinteger functions is caused by a poor choice of algorithms. It computes a larger order derivative to find the answer. Should use a different algorithm such as the one in A&S 10.1.8 and 10.1.9.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=736535&group_id=4933 