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

 Method (no overloads)

Summary

expr read as a constant times F^E times a whole power of a
linear L, with every x in E inside a reciprocal power of L:
the constant, F, E written in u = 1/L, u, L, its slope
and the power of L. The exponent is rewritten into u a node at a time --
b/L^k is b u^k -- rather than by substituting x = (1/u - c)/d and
asking the simplifier to see that 1/(1/u)^2 is u^2.

Remarks

A whole power of another linear M = p + q x is read too, as M/L written in
u times L: with L = c + d x, M/L = ((d p - q c) u + q)/d, a
linear in u, so M^k adds k to the power of L and
((d p - q c) u + q)^k to Beside, and -k to its power of d, kept
apart from the constant so that the caller writes one power of d, not d/d.
Beside is null when there is no such factor. A quotient N/L^k in the exponent with N linear is
(N/L) u^(k - 1) the same way. Rubi's 2.3 f^(c/(a + b x)) x^m,
F^(a + b/(c + d x))/(e + f x)^m and F^(e + f (a + b x)/(c + d x))/(g + h x)^m were declined, for want of the other linear.
https://github.com/asc-community/AngouriMath/issues/233

























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