hyp2exp
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09-05-2022, 11:50 AM
Post: #4
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RE: hyp2exp
(09-04-2022 08:00 PM)parisse Wrote: No, but it's fairly easy: subst(expression,exp,cosh+sinh) Above exp2hyp expression might be "simplified" to sin/cos Just keep in mind, e^(i*x) = cos(x) + i*sin(x) = cosh(i*x) + sinh(i*x) cos(x) = cosh(i*x) i*sin(x) = sinh(i*x) cosh(x) = cos(i*x) i*sinh(x) = sin(i*x) CAS> subst(e^(i*x), exp, x -> cosh(x) + sinh(x)) cos(x) + i*sin(x) --- Same trick can be used for a "better" exp2trig CAS> f := e^x - e^-x // = 2*sinh(x) CAS> exp2trig(f) → e^x - e^-x CAS> f(exp = (x -> cos(i*x) + sin(i*x)/i)) → -2*i*sin(i*x) Or, in steps, since sinh/cosh tends to "simplify" to sin/cos CAS> f(exp=cosh+sinh)(x=x/i)(x=x*i) → -2*i*sin(i*x) |
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Messages In This Thread |
RE: hyp2exp - parisse - 09-04-2022, 08:00 PM
RE: hyp2exp - robmio - 09-05-2022, 07:21 AM
RE: hyp2exp - parisse - 09-05-2022, 12:40 PM
RE: hyp2exp - robmio - 09-13-2022, 04:00 PM
RE: hyp2exp - Albert Chan - 09-05-2022 11:50 AM
RE: hyp2exp - robmio - 09-09-2022, 11:46 AM
RE: hyp2exp - Albert Chan - 09-05-2022, 04:25 PM
RE: hyp2exp - parisse - 09-14-2022, 05:48 PM
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