Not enough Input arguments in integral function

Good afternoon,

I am trying to compute the exact Wagner function on MATLAB with the following equation : , where c(k) is the Theodorsen function. I already created a function computing c(k), but I am having trouble computing the integral. I have defined k = 0.1 and s = linspace(0,100,100).

For now I have tried two options with the integral(fun, xmin, xmax) function of MATLAB :

1) Create a function in another matlab script and then write W = (2./pi).*integral(fun_W,0, Inf). The result was an error saying :

"Not enough input arguments.

Error in W_integrande (line 2)

f = F_k(k).*sin(k.*s)./k;

Error in HMWK3_DUMAS (line 14)

W = (2./pi).*integral(W_integrande,0, Inf)"

2) On another forum I saw people using

"fun_W = @(k,s) real(c_k(k)).*sin(k.*s)./k;

W = (2./pi).*integral(fun_W,0, Inf)"

So I tried it and this time the error is

"Not enough input arguments.

Error in HMWK3_DUMAS>@(k,s)real(c_k(k)).*sin(k.*s)./k (line 13)

fun_W = @(k,s) real(c_k(k)).*sin(k.*s)./k;

Error in integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 83)

[q,errbnd] = vadapt(@AToInfInvTransform,interval);

Error in integral (line 87)

Q = integralCalc(fun,a,b,opstruct);

Error in HMWK3_DUMAS (line 14)

W = (2./pi).*integral(fun_W,0, Inf);"

I don't understand why I am getting the error "not enough input arguments", could someone help me with this ?

Thank you in advance !

[David Hill]

It would be helpful if you provided your function for c(k).

[Alix DUMAS]

Sure ! My function for c(k) is :

function[c] = c_k(k)

c = besselh(1,2,k)./(besselh(1,2,k)+j.*besselh(0,2,k));

end

Answer 1

[David Hill]

s=0:100;
for t=1:numel(s)
    fun_W=@(k)real(c_k(k))./k.*sin(k*s(t));
    W(t)=2/pi*integral(fun_W,0,Inf);
end





function c= c_k(k)
    c = besselh(1,2,k)./(besselh(1,2,k)+1j.*besselh(0,2,k));%need 1j
end

[Alix DUMAS]

Thank you it worked really well !