AngouriMath
SolveAnExponentialOfASymbolicMultipleOfAnArctangentAsPowersOfTheLinears(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
An exponential of a symbolic multiple of i arctan(L) , L linear, beside
powers of multiples of1 + L^2 , written as powers of the two linears:
e^(k i arctan(L)) is (1 + i L)^(k/2) (1 - i L)^(-k/2) and
(K (1 + L^2))^q is K^q (1 + i L)^q (1 - i L)^q , each exactly for a real
L and any k and q : the two principal arguments are
arctan(L) and its negative, and 1 + L^2 is positive.
powers of multiples of
Remarks
Rubi's 5.3.6 (c + a^2 c x^2)^p/e^(2 i p arctan(a x)) is then
c^p (1 - i a x)^(2p) , a power of a linear; it was left unevaluated.
SolveByWritingAnExponentialOfAnInverseAlgebraically(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) takes a rational
multiple, and this the rest.
https://github.com/asc-community/AngouriMath/issues/718
SolveByWritingAnExponentialOfAnInverseAlgebraically(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) takes a rational
multiple, and this the rest.
https://github.com/asc-community/AngouriMath/issues/718
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