write these functions (p(ρ,τ)=a(τ)e^(-ρb(τ))@a(τ)={(γe^βτ)/(β(e^γτ-1)+γ)}^α@b(τ)=(e^γτ-1)/(β(e^γτ-1)+γ)@γ=√((κ+λ)^2+2σ^2 )@β=(κ+λ+γ)/2@α=2κθ/σ^2 .) in matlab

Here is the implementation of the given functions in MATLAB:

main.m
function result = p(rho, tau, kappa, lambda, sigma, theta)
    gamma = sqrt((kappa + lambda)^2 + 2 * sigma^2);
    beta = (kappa + lambda + gamma) / 2;
    alpha = 2 * kappa * theta / sigma^2;
    a = (gamma * exp(beta * tau)) / ((beta * (exp(gamma * tau) - 1)) + gamma)^alpha;
    b = (exp(gamma * tau) - 1) / ((beta * (exp(gamma * tau) - 1)) + gamma);
    result = a * exp(-rho * b);
end
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You can call the function p by passing the following arguments:

• rho: Scalar or matrix of size MxN - rho values
• tau: Scalar or matrix of size MxN - tau values
• kappa: Scalar - kappa value
• lambda: Scalar - lambda value
• sigma: Scalar - sigma value
• theta: Scalar - theta value

For example:

main.m
result = p(0.5, 1, 1, 1, 1, 1);
disp(result);
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This will output the result of the p function for given input values.

Note: Make sure to define all the required parameters before calling the function.