Integral of function with Bessel function. 0 to infinity
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So I'm quite new to Matlab and just want to solve a function using a few different parameters.
The function is:
where Iq(.) is the modified Bessel function of the first kind of order q.
I cant seem to get any good answer from the code below:
syms x
theta=0.1;
V_t=0.02;
kappa=1;
tau=30/365;
sigma=0.1425;
B=((1-exp(-kappa*tau))/(kappa*tau));
c=(2*kappa)/((sigma^2)*(1-exp(-kappa*tau)));
u=c*V_t*exp(-kappa*tau);
q=((2*kappa*theta)/(sigma^2))-1;
f= (sqrt(((1-B)*theta)+B*x)*c*exp(-u-(c*x))*((u/(c*x))^q/2))*(besseli(q,(2*sqrt(u*(c*x)))));
int(f, 0, inf)
all i get is
ans =
int((2744904123399207*exp(- (2744904123399207*x)/2199023255552 - 6472494767983165/281474976710656)*((8646976715685959*x)/9007199254740992 + 4610848499904423/1152921504606846976)^(1/2)*besseli(28751/3249, 2*((17766377577316783221931550350155*x)/618970019642690137449562112)^(1/2))*(6472494767983165/(351347727795098496*x))^(28751/3249))/4398046511104, x, 0, Inf)
Please help me!
1 Comment
Yu Jiang
on 9 Aug 2014
Hi Sebastian
To let me better help you, could you let me know what is the definition of I_q? It does not seem to be besseli(q,(2*sqrt(u*(c*x))), since besseli(q,(2*sqrt(u*(c*x))) is not a number when x=10.
-Yu
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