Question 26 (Programming) The Gaussian error function. Erfly) is defined as Question 27 (Programming) The Catalan numbers form a sequence of natural numbers that occur in various counting problems The Catalan sequence can be defined as follows: Your goal is to write a C program to compute Erf(y for various values of y. Please follow the following steps: (a 3marks) Write a function to compute the integrand of the above function (e). The zeroth element of the series is: Co = 1 Subsequent elements are defined as: The function should have the following prototype: double Antegrand tdoublo x) Cn+1 = 2 * (2 * n + 1) * Cn / (n + 2) (b) (3 marks) Write a general-purpose implementation of any integration algorithm you've seen in this elass (midpoint, trapezoidal, Simpson, or Monte Carlo). It should have the following prototype: The first few numbers in the sequence are double integral(DED fp, double a, double b, int n 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, . Where DED is defined as: typedet double DED(double) Write a C program which computes and prints the Catalan sequence from the zeroth number up to the nth number in the sequence, where n is a value input by the user fp is a pointer to the function you would like to integrate, a is the left bound, b is the right bound, and n is the number of panels. (c 3 marks) Write a function that uses the integral function to evaluate Erf(y) It should Bonus (5 marks): If you define a recursive function to compute the nth Catalan number you can get 5 bonus points. I would suggest first doing it directly and then defining this function if you still have time. have the following prototype double BrE (double y Use n-500 panels. (d) (4marks) Write a perogram to read a value, y and evaluate the erroe function at that value. It should output the value read and the value of the error function