Group Description

A series expansion is a representation of a particular function as a sum of powers in one of its variables, or by a sum of powers of another (usually elementary) function f(x).

An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily good approximation to a given function for large enough x.

Asymptotic series can be computed by doing the change of variable x -> 1/x and doing a series expansion about zero. Many mathematical operations can be performed on asymptotic series. For example, asymptotic series can be added, subtracted, multiplied, divided (as long as the constant term of the divisor is nonzero), and exponentiated, and the results are also asymptotic series (Gradshteyn and Ryzhik 2000, p. 20).

Interface

#include <codecogs/maths/algebra/series/asympt_expn.h>

using namespace Maths::Algebra::Series;

	double	bcorr (double a, double b) Evaluate Del(a) + Del(b) - Del(a+b).
	Real	cc_bcorr (Real a, Real b) This function is available as a Microsoft Excel add-in.
	double	asympt_expn (double a, double b, double lambda, double eps) Asymptotic Series Expansion for ix(a,b) for large a and b.
	Real	cc_asympt_expn (Real a, Real b, Real lambda, Real eps) This function is available as a Microsoft Excel add-in.

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Function Documentation

Evaluates where

Parameters:

a	argument 1
b	argument 2

Note:

It is assumed that a >= 8 and b >= 8.

Authors:

Barry W. Brown, James Lovato, Kathy Russell
Updated by Vince Cole
Documentation by Nick Owens

Source Code:

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Asymptotic Series Expansion for ix(a,b) for large a and b

Parameters:

a	argument 1
b	argument 2
lambda	argument 3
eps	tolerance

Note:

It is assumed that lambda is non-negative and that a and b are greater than or equal to 15.

Authors:

Barry W. Brown, James Lovato, Kathy Russell
Documention by Nick Owens, Vince Cole

Source Code:

- To get code register with CodeCogs. Already a Member, then Login.