CodeCogs

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

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Interface

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

using namespace Maths::Approximation::Series;

double bcorr( double a, double b )
double asympt_expn( double a, double b, double lambda, double eps )

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 (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).

FUNCTION

bcorr

Evaluates

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

(1)

where

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

(2)

Parameters

argument 1

argument 2

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

Author

Barry W. Brown, James Lovato, Kathy Russell

Author

Updated by Vince Cole

Author

Documentation by Nick Owens

Interactive Calculator

Result –

FUNCTION

asympt_expn

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

Parameters

argument 1

argument 2

lambda

argument 3

eps

tolerance

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

Author

Barry W. Brown, James Lovato, Kathy Russell

Author

Documention by Nick Owens, Vince Cole

Interactive Calculator

lambda

eps

Result –