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# eulergamma

Euler-Mascheroni constant

## Description

example

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

collapse all

### Euler-Mascheroni Constant

The Euler-Mascheroni constant is defined as follows:

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

## 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