trigreduce(sinh(z)^4)



Geordie McBain <geordie.mcbain@aeromech.usyd.edu.au> writes:

>   There is an erroneous reduction rule for a hyperbolic multiple-angle
>   formula:
>   
> (C1) trigreduce(sinh(z)^4);
> 			 - COSH(4 z) + 4 COSH(2 z) - 3
> (D1) 			 -----------------------------
> 				       8
> 
>   This is -1 times the correct answer.

[...]

>   Cosh(z)^4, sin(z)^4, and sinh(z)^n (n=2, 3, 5, 6) are all reduced
>   correctly, but sinh(z)^8 has a similar error.

This should fix it (BTW, this implies that the original definition in
trgred.lisp gives the correct result iff n = 2,3 mod 4, so sinh^5 is
also wrong).

(DEFUN SINH^N (%N V)
  (M* (m^ -1 (// %n 2))
      (SC^N %N V (COND ((ODDP %N) '(%SINH))
		       ('(%COSH)))
	    (NOT (ODDP %N))
	    (M^ -1 (M+ (// %N 2) 'K)))))

For odd n this is still more complicated than necessary, though.

Wolfgang