eulergamma

Euler–Mascheroni constant

Syntax

eulergamma

Description

eulergamma represents the Euler–Mascheroni constant. To get a floating-point approximation with the current precision set by digits, use vpa(eulergamma).

Examples

Represent and Numerically Approximate the Euler–Mascheroni Constant

Represent the Euler–Mascheroni constant using eulergamma, which returns the symbolic form eulergamma.

eulergamma

ans =
eulergamma

Use eulergamma in symbolic calculations. Numerically approximate your result with vpa.

a = eulergamma;
g = a^2 + log(a)
gVpa = vpa(g)

g =
log(eulergamma) + eulergamma^2
gVpa =
-0.21636138917392614801928563244766

Find the double-precision approximation of the Euler–Mascheroni constant using double.

double(eulergamma)

ans =
    0.5772

Show Relation of Euler–Mascheroni Constant to Gamma Functions

Show the relations between the Euler–Mascheroni constant γ, digamma function Ψ, and gamma function Γ.

Show that $$\gamma =-\Psi \left(1\right)$$.

-psi(sym(1))

ans =
eulergamma

Show that $$\gamma =-\Gamma \text{'}\left(x\right)|{}_{x=1}$$.

syms x
-subs(diff(gamma(x)),x,1)

ans =
eulergamma

More About

Euler–Mascheroni Constant

The Euler–Mascheroni constant is defined as follows:

$$\gamma =\underset{n\to \infty }{\lim }\left(\left({\displaystyle \sum _{k=1}^n\frac{1}{k}}\right)-\ln \left(n\right)\right)$$

Tips

• For the value e = 2.71828…, called Euler’s number, use exp(1) to return the double-precision representation. For the exact representation of Euler’s number e, call exp(sym(1)).

• For the other meaning of Euler’s numbers and for Euler’s polynomials, see euler.

Version History

Introduced in R2014a