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SolveAPolynomialOverHighWholePowersOfTwoLinears(AngouriMath.Entity,AngouriMath.Entity.Variable)

Method (no overloads)

Summary

A polynomial over high whole powers of two linears, P(x)/(L1^m L2^n) with
m + n = k past FewestLinearPowersWrittenInTheirQuotient and P of degree
at most k - 2, under t = L1/L2: a polynomial in t over a power of it.
Rubi's x^2/((1 - a x)^16 (1 + a x)^11).

Remarks

With D = a1 b2 - a2 b1, x = (a1 - a2 t)/(b2 t - b1), L2 = D/(b2 t - b1) and dx = -D dt/(b2 t - b1)^2, the integrand is -D^(1 - k) t^(-m) S(t) dt for
S(t) = sum_j p_j (a1 - a2 t)^j (b2 t - b1)^(k - 2 - j), as
SolveTwoLinearPowersWhoseExponentsSumToAWholeNumber(AngouriMath.Entity,AngouriMath.Entity.Variable) has it for exponents
that are not whole. Here they are, so each t^(i - m) is L1^(i - m) L2^(m - i) exactly, and the one at i = m - 1 integrates to ln(L1) - ln(L2).
The partial fractions take the two linears apart with a symbol in them over k terms, and
ran past the budget at k = 27; below the bound they answer in their own form, and
this leaves them to it, as it leaves numbers to Hermite's reduction. The answer is
differentiated back at sampled points.
https://github.com/asc-community/AngouriMath/issues/233

AngouriMath

Table of contents

AngouriMath

SolveAPolynomialOverHighWholePowersOfTwoLinears​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

SolveAPolynomialOverHighWholePowersOfTwoLinears(AngouriMath.Entity,AngouriMath.Entity.Variable)