User:Remorse

 $f(x)=\underset{0}{\overset{\mathrm{\infty }}{\int }}\frac{e^{-t}{t}^{x-1}}{\mathrm{\Gamma }(x)}dt+\sum _{n=1}^{\mathrm{\infty }}\frac{(-1{)}^n}{n!}\prod _{k=0}^n\frac{(2k+1{)}^2+x^2}{(2k+2)!}+\frac{1}{1-e^{-x}}\prod _{m=1}^{\mathrm{\infty }}{(1+\frac{x^2}{m^2{\pi }^2})}^{-1}+\sqrt{\frac{x^2+1}{x^2+2}}\cdot \frac{\ln (x^2+3)}{\sqrt[3]{x^2+4}}+\frac{\sin (x)}{x}+\frac{\cos (x)}{x^2+1}$