Special functions¶
-
Gamma
(x)¶ -
Note
Euler’s constant is represented by
gamma
in yacas.- Example
In> Gamma(1.3) Out> Gamma(1.3); In> N(Gamma(1.3),30) Out> 0.897470696306277188493754954771; In> Gamma(1.5) Out> Sqrt(Pi)/2; In> N(Gamma(1.5),30); Out> 0.88622692545275801364908374167;
See also
()
,gamma
-
Zeta
(x)¶ -
- Example
In> Precision(30) Out> True; In> Zeta(1) Out> Infinity; In> Zeta(1.3) Out> Zeta(1.3); In> N(Zeta(1.3)) Out> 3.93194921180954422697490751058798; In> Zeta(2) Out> Pi^2/6; In> N(Zeta(2)); Out> 1.64493406684822643647241516664602;
See also
()
-
Bernoulli
(n)¶ -
Bernoulli
(n, x)
-
Euler
(n)¶ -
Euler
(n, x) Euler numbers and Euler polynomials
- Example
In> Euler(6) Out> -61; In> A:=Euler(5,x) Out> (x-1/2)^5+(-10*(x-1/2)^3)/4+(25*(x-1/2))/16; In> Simplify(A) Out> (2*x^5-5*x^4+5*x^2-1)/2;
See also
-
LambertW
(x)¶ -
- Example
In> LambertW(0) Out> 0; In> N(LambertW(-0.24/Sqrt(3*Pi))) Out> -0.0851224014;
See also