olya

#include <iostream>
#include <conio.h>
#include <math.h>
#include <iomanip>
#include <cstdlib>
#include <cmath>
#define LC_CTYPE
#define _USE_MATH_DEFINES
#include<cmath>
# define M_PI 3.14159265358979323846

using namespace std;
double pi = 3.14159265358979323846;


double myf(int n, double x) {
    int a = (2 * n);
    return (((a - 1) * (a - 1)) - (x * x)) / (((a + 1) * (a + 1)) - (x * x));
}

double f(double x, double e) {
    double z1 = 0;
    double z2 = 1 / (1 - x * x);
    int n = 2;
    double k = myf(n, x);
    double res = z1 + z2;
    while (abs(z2 - z1) >= e)
    {
        z1 = z2;
        z2 = z1 * k;
        cout << z1 << " " << k << " " << z2 << endl;
        res += 1/ (((2*n - 1) * (2*n - 1)) - (x * x));
        n++;
        k = myf(n, x);
    }
    return ((4 * x) / (pi)) - res;
}

double F(double x) {
    return tan((pi * (x-(int)x) / 2.0));
}


int main() {
    setlocale(LC_ALL, "rus");
    double inf = numeric_limits<double>::infinity();
    double x_start, x_end, dx, x_ideal;
    double e;
    cout << "Введите начальное значение x:" << endl;
    cin >> x_start;
    while (!cin) {
        cin.clear();
        cout << "Введите корректное значение:" << endl;
        cin >> x_start;
    }

    cout << "Введите конечное значение x:" << endl;
    cin >> x_end;
    while (!cin || x_end == x_start) {
        cin.clear();
        cout << "Введите корректное значение:" << endl;
        cin >> x_end;
    }

    cout << "Введите шаг:" << endl;
    cin >> dx;
    while (!cin || ((dx < 0) & (x_start < x_end)) || ((dx > 0) & (x_start > x_end)) || (abs(x_start - x_end) < abs(dx)) || dx == 0) {
        cin.clear();
        cout << "Введите корректное значение:" << endl;
        cin >> dx;
    }

    cout << "Введите точность:" << endl;
    cin >> e;
    while (!cin || e <= 0) {
        cin.clear();
        cout << "Введите корректное значение:" << endl;
        cin >> e;
    }

    cout << "f(x) = f(x-1)*(((a-2)*(a-2))-(x*x))/((a*a)-(x*x))), где a=2n-1" << "\n";
    cout << "F(x) = tg((pi*x)/2) " << "\n";

    cout << " _________________________________________________________________________________________________" << endl;
    cout << "|" << setw(12.5) << "x" << setw(12.5) << "|" << setw(13.5) << "f(x)" << setw(11.5) << "|" << setw(14) << "F(x)" << setw(11) << "|" << setw(15) << "delta" << setw(10) << "|" << endl;
    cout << " _________________________________________________________________________________________________" << endl;
    for (double i = x_start; i <= x_end + 0.000001; i += dx) {
        double f1 = f(i, e);
        double F1 = F(i);
        double del;
        if ((f1 == inf && F1 == inf) || f1 == -inf && F1 == inf) {
            del = INFINITY;
        }
        else {
            del = sqrt(abs(f1 * f1 - F1 * F1));
        }

        cout << fixed << setprecision(6);
        cout << "|" << setw(12.5) << i << setw(12.5) << "|" << setw(13.5) << f1 << setw(11.5) << "|" << setw(14) << F1 << setw(11) << "|" << setw(15) << del << setw(10) << "|" << endl;
        cout << " _________________________________________________________________________________________________" << endl;
    }
    cout << "Введите значение x_ideal:" << endl;
    cin >> x_ideal;
    while (!cin) {
        cin.clear();
        scanf_s("%*[^\n]");
        cout << "Введите корректное значение:" << endl;
        cin >> x_ideal;
    }
    cout << " _________________________________________________________________________________________________" << endl;
    cout << "|" << setw(12.5) << "eps" << setw(12.5) << "|" << setw(13.5) << "f(x_ideal)" << setw(11.5) << "|" << setw(14) << "F(x_ideal)" << setw(11) << "|" << setw(15) << "delta" << setw(10) << "|" << endl;
    cout << " _________________________________________________________________________________________________" << endl;

    for (double i = 0.1; i >= 0.0000001; i = i / 10) {
        double f1 = f(x_ideal, i);
        double F1 = F(x_ideal);
        double del;
        if (f1 == inf && F1 == inf) {
            del = INFINITY;
        }
        else {
            del = sqrt(abs(f1 * f1 - F1 * F1));
        }
        cout << fixed << setprecision(6);
        cout << "|" << setw(12.5) << i << setw(12.5) << "|" << setw(13.5) << f1 << setw(11.5) << "|" << setw(14) << F1 << setw(11) << "|" << setw(15) << del << setw(10) << "|" << endl;
        cout << " _________________________________________________________________________________________________" << endl;
    }
}