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SolveByWritingATrigonometricFunctionOfAnImaginaryLogarithmInExponentials(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)

Method (no overloads)

Summary

A trigonometric function of a + b ln(u) with an imaginary b, written in
exponentials: e^(i (a + b ln(u))) is e^(i a) times the real power
u^(i b), so the sine, cosine and the rest are sums and quotients of powers of
u, which the rules for those answer.

Remarks

sin(a + ln(c x^2) sqrt(-1/4)) and tan(a + i ln(x)) were declined: the closed
form for a power of the variable times a sine or cosine of a logarithm divides by
(m + 1)^2 + B^2, which an imaginary B makes zero, and Rubi's 4.7.5 has 62
problems built on exactly that, with b = sqrt(-(m + 1)^2/n^2). In exponentials the
zero is a power of x that is 1/x, and its integral a logarithm. Only for a
number: a real b is the closed form's, after which this is asked, and a symbolic
one, sqrt(-1/n^2), makes the zero one that only a sign of n decides.
https://github.com/asc-community/AngouriMath/issues/718

AngouriMath

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AngouriMath

SolveByWritingATrigonometricFunctionOfAnImaginaryLogarithmInExponentials​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

SolveByWritingATrigonometricFunctionOfAnImaginaryLogarithmInExponentials(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)