Evaluate F(x) Using Recursion in C – Series Expansion with Factorial

Introduction

In this tutorial, you will learn how to evaluate the function F(x) using recursion in C, where

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C Program to Evaluate F(x) Using Recursive Calls

#include <stdio.h>
#include <math.h>

double factorial(int n) {
    if (n == 0 || n == 1)
        return 1;
    return n * factorial(n - 1);
}

double power(double x, int n) {
    if (n == 0)
        return 1;
    return x * power(x, n - 1);
}

double evaluateFx(double x, int n) {
    if (n == 1)
        return x;
    return evaluateFx(x, n - 2) + pow(-1, (n - 1) / 2) * power(x, n) / factorial(n);
}

int main() {
    double x;
    int n;

    printf("Enter value of x: ");
    scanf("%lf", &x);

    printf("Enter the highest odd value of n: ");
    scanf("%d", &n);

    if (n % 2 == 0) {
        printf("Please enter an odd number for n.\n");
        return 1;
    }

    double result = evaluateFx(x, n);
    printf("F(x) = %.6lf\n", result);

    return 0;
}

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Explanation

• factorial(n): Calculates n! using recursion.
• power(x, n): Computes xⁿ using recursion.
• evaluateFx(x, n): Recursively evaluates the alternating series up to term xⁿ/n!.

The series alternates between addition and subtraction based on term index and uses odd values of n only (e.g., 1, 3, 5, …).

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Sample Output

Enter value of x: 2  
Enter the highest odd value of n: 7  
F(x) = 1.508314

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Use Cases

• Approximating functions like sin(x) or Taylor series expansion.
• Learning recursion with real-world math-based examples.
• Helpful in competitive programming and academic exercises.