AngouriMath
SolveAPolynomialInASineOverAPowerOfABinomialInItInPowersOfTheBinomial(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
A polynomial in a sine or a cosine of a linear over a whole power of a binomial in it,
(A + B cos(y) + C cos(y)^2)/(a + b cos(y))^4 , written in powers of the binomial:
withu = a + b f , f = (u - a)/b , and P(f)/u^n = sum c_j u^(j - n) with
c_j = sum_(i >= j) p_i C(i, j) (-a)^(i - j)/b^i , each power of the binomial its own
question.
with
question.
Remarks
The rules after it took the whole quotient through the half-angle and wrote 30 million
characters for(A + B cos(x) + C cos(x)^2)/(a + b cos(x))^4 in eighteen seconds, where
1/(a + b cos(x))^4 alone is 44 thousand. Rubi's 4.1.4 and 4.2.4
(a + b cos)^m (A + B cos + C cos^2) at m = -4 timed out. An even whole power
of the other function above the bar is a power of1 - f^2 , exactly, and read as
one: Rubi's 4.1.2.2cos(c + d x)^6 sin(c + d x)^3/(a + b sin(c + d x))^2 and its
kin timed out too, where in the sine each is the polynomial over the power.
https://github.com/asc-community/AngouriMath/issues/718
https://github.com/asc-community/AngouriMath/issues/233
characters for
of the other function above the bar is a power of
one: Rubi's 4.1.2.2
kin timed out too, where in the sine each is the polynomial over the power.
https://github.com/asc-community/AngouriMath/issues/718
https://github.com/asc-community/AngouriMath/issues/233
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