Equation involving Incomplete Gamma function

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Sudhir Sahoo
Sudhir Sahoo 2021-3-31
回答： Nipun 2024-6-6
How to solve this equation using matlab
where and and here m, , are constant.
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Sudhir Sahoo
Sudhir Sahoo 2021-4-1
Hello thanks for your comment. @Star Strider However, here m is constant and only b and a are function of θ. hence θ is the only variable.
Star Strider
Star Strider 2021-4-1
O.K. I missed seeing that m was constant. Code the expression and solve it in terms of only θ.

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Nipun
Nipun 2024-6-6
Hi Sudhir,
I understand that you want to solve the given equation in MATLAB comprising of trigonometric and incomplete gamma functions.
I recommend using the "symbolic Math Toolbox" in MATLAB to create the equation and using a MATLAB solver to solve for "theta". MATLAB supports incomplete gamma functions using an in-built function, called "gammainc".
Here are the steps you may take to slve the given equation:
  1. Create symbolic variables
  2. Code the equation
  3. Use solver to solve for "theta"
I am attaching a code snippet with this answer for your reference:
syms theta m tmin tmax
a = 2*sin(theta).^2
b = (cos(theta)-sin(theta)).^2/2
% Equation (split into two parts)
part1 = (4/(cot(theta)-1).^2)^((m+2)/(m+3))
arg1 = (m+1)/(2*m+6);
arg2 = b*tmin/2;
arg3 = a*tmin/2;
arg4 = b*tmax/2;
arg5 = a*tmax/2;
part2_numerator = gammainc(arg1, arg2) - gammainc(arg1, arg4);
part2_denominator = gammainc(arg1, arg3) - gammainc(arg1, arg5);
part2 = part2_numerator/part2_denominator;
% creating equation
eqn = part1*part2
% Solving
ans = solve(eqn, theta);
For more information on the in-built functions, refer to the following MathWorks documentation:
  1. Symbolic Toolbox: https://www.mathworks.com/help/symbolic/syms.html#d126e328782
  2. Incomplete Gamma Function: https://www.mathworks.com/help/matlab/ref/gammainc.html
  3. Equation Solver: https://www.mathworks.com/help/symbolic/sym.solve.html
Hope this helps.
Regards,
Nipun

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