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asympt expn

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

Info

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

 
doublebcorrdoublea
doubleb )
Evaluates where

Note

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

Parameters

aargument 1
bargument 2

Authors

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

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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Asympt Expn

 
doubleasympt_expndoublea
doubleb
doublelambda
doubleeps )
Asymptotic Series Expansion for ix(a,b) for large a and b

Note

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

Parameters

aargument 1
bargument 2
lambdaargument 3
epstolerance

Authors

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

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.