Thanks for the elaboration. How do you do this step: "I inferred polynomials of t from the columns, giving a polynomial in both x and t." ? Thanks, Dan On 2013-07-23, at 10:37 PM, Steve Witham wrote:
From: Dan Asimov <dasimov@earthlink.net>
What method or formula are you using to get the Taylor coefficients of expm1^t at x = 1/2, where expm1(x) := e^x - 1 ??? (I don't know what sympy is or what query you have submitted to it.)
I've sent a more detailed answer to Dan.
The short story is,
I started with N (around 18) terms of the Taylor series of f(x) = e^((x+e)/e) - e P = x + x^2/(2! e) + x^3/(3! e^2) ...
I generated M polynomials, for 0 through M-1 iterations of P, each up to N terms. (I'm forgetting whether M needs to be N+1 or N-1 right now.)
Visualize an array of the coefficients, with the iterations as rows. Say t is the row number, starting at zero.
The column for the constant term is all zero. the coefficient of x is all 1, constant down the column x^2, a linear progression x^3, a quadratic x^4, a cubic ...
I inferred polynomials of t from the columns, giving a polynomial in both x and t.