Exercise "math"

1. Calculate (using C mathematical functions):
   • Γ(5) (Gamma function). Hint: man -k gamma.
   • J₁(0.5) (Bessel function). Hint: man -k bessel.
   • √-2, eⁱ, e^iπ, i^e.

   Hints:

   • There is no built-in format for complex numbers, you have to print separately the real and the complex parts using creal, creall, cimag, cimagl functions (read man creal and man cimag).
   • The header file complex.h defines the imaginary unit as I.
   • In some implementations the header math.h defines M_E (the value of e) and M_PI (the value of π). If not, you can define this constants (in double precision) as

     # define M_E  2.7182818284590452354 /* e */
     # define M_PI 3.1415926535897932384 /* pi */
     

2. Find out how many signigicant digits can variables of types float, double, and long double hold in them by trying to store the number 0.1111111111111111111111111111 in the variable and then printing out what is stored. The long double number must end with L:

   long double x = 0.1111111111111111111111111111L;
   

   otherwise it will be considered as double and truncated. Print numbers with format placeholders "%.25g" for float, "%.25lg" for double, "%.25Lg" for long double.