def integ(alpha, b): """ :param alpha: :param b: :return: integral of -alpha * b * e^(-x) * x ^(-alpha-1), from b to infty That is the integral of e^-W+ from b to infty That is E[e^[-W+]] """ result = integrate(sp_exp(-x) * x**(-alpha - 1), (x, b, float("inf"))) result *= -alpha * b**alpha return result
########################################################### from pathlib import Path reproduced_results = Path("reproduced-results") from sympy import exp as sp_exp from sympy import symbols as sp_symbols from sympy import Rational as sp_Rational from sympy import lambdify as sp_lambdify from IPython.display import display import numpy as np from collections import defaultdict n = sp_symbols('n') psis = [sp_exp(-1 / n), 1 - sp_exp(-n)] psi_codes = { psis[0]: 'exp((NType)(-1./ln))', psis[1]: '1. - exp(-(NType)ln)', } Gs = {psis[0]: [-3.6], psis[1]: [-1.4, -1.6]} Ls = [255] E6_P2F6_sym = sp_symbols("\\boldsymbol{E}^{(6)}_{P2\,F6}") E8_P2F8_sym = sp_symbols("\\boldsymbol{E}^{(8)}_{P2\,F8}") E6_P4F6_sym = sp_symbols("\\boldsymbol{E}^{(6)}_{P4\,F6}") E8_P4F6_sym = sp_symbols("\\boldsymbol{E}^{(8)}_{P4\,F6}") stencil_string = {