asympt expn

Evaluate Del(a) + Del(b) - Del(a+b).

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Contents

Interface
Bcorr
Asympt Expn
Page Comments

Dependents

Interface

C++

Overview

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 (Erdlyi 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).

Bcorr

doublebcorr(	double	`a`
	double	`b`	)

Evaluates

$\Delta(a) + \Delta(b) - \Delta(a + b)$

(2)

where

$\Delta(x) = x + \ln(\Gamma(x)) + (x-0.5) \ln(x) + \frac{ \ln(2 \pi)}{2}$

(3)

Note

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

Parameters

a	argument 1
b	argument 2

Authors

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

Source Code

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Asympt Expn

doubleasympt_expn(	double	`a`
	double	`b`
	double	`lambda`
	double	`eps`	)

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