4321.sagews

f(x,n) = (gamma((n+1)/2)*((1+((x^2)/2))^(-(n+1)/2)))/(sqrt(pi*n)*gamma(n/2))

f.show()

\newcommand{\Bold}[1]{\mathbf{#1}}\left( x, n \right) \ {\mapsto} \ \frac{{\left(\frac{1}{2} \, x^{2} + 1\right)}^{{\left(-\frac{1}{2} \, n - \frac{1}{2}\right)}} \Gamma\left(\frac{1}{2} \, n + \frac{1}{2}\right)}{\sqrt{\pi n} \Gamma\left(\frac{1}{2} \, n\right)}

#Example
f(1,2).n()

0.192450089729875

#Plotting
P1 = plot(f(x,1),(x,-10,10), color='green')
P2 = plot(f(x,3),(x,-10,10), color='red')
P1 + P2