How to calculate very large number by Matlab

I want to find S_1+S_2+S_3

[Torsten]

Please supply the above graphics as code or at least as a plain ascii text so that we don't need to type it again.

[James Tursa]

Replaced with larger image.

[James Tursa]

@Fatima Majeed Have you written any code for this yet?

[Fatima Majeed]

% Given values
H = 3000175332800;
D = 0.9999932;
x = exp(2.8 * 10^10);
C_1 = 17.362;
C_2 = 2.077;
B_2 = 0.18525;

% Calculations
R = (log(x))^(3/5) / (log(log(x)))^(1/5);
S_1 = x^(-0.5) * (log(H / (2 * pi)))^2 / (2 * pi) + x^(D - 1) * ((B_2 * R - log(2))^2 / (2 * pi) - (log(H / (2 * pi)))^2 / (2 * pi) + 2.394);
S_2 = 2 * (C_1 * exp(B_2 * (5 - 8 * D) * R / 3) * (B_2 * R)^(5 - 2 * D) + C_2 * exp(-B_2 * R) * (B_2 * R)^2);
S_3 = 1.197 * log(x) / (B_2 * R);
b = (exp(B_2 * (5 - 8 * D) * R / 3) * (B_2 * R)^(5 - 2 * D))^(-1) * (S_1 + S_2 + S_3);

% Display the result
fprintf('The value of b is: %.6f\n', b);

The value of b is: NaN

[KSSV]

x = exp(2.8 * 10^10);

The above will lead to inf.....Are you sure you want that?

[Fatima Majeed]

yeh, I want to calculate in the end the value of S_1+S_2+S_3.But my problem is with that also with the value of H

[Steven Lord]

Even if you try to operate on this symbolically, it's extremely large.

x = exp(sym(2.8e10))

x = 

vpa(x, 10)

ans = 

∞

numberOfDigits = vpa(log10(x))

numberOfDigits = 

12160245493.291051174231609729665

If you were able to write out x it would have over twelve billion digits.

What's the purpose of this calculation? What does S1+S2+S3 represent? I'd consider trying to find another way to compute that quantity that doesn't require combining numbers that vary by so so many orders of magnitude.

[Fatima Majeed]

I am reading this paper https://doi.org/10.48550/arXiv.2204.01980 on the page 13 he wanted to calculate A(x,delta) to bound

\[

\left| \frac{\psi(x) - x}{x} \right|

\]