Erlang b formula continuous

Hello,

I'm trying to use a continuous form of Erlang B formula in my code as a function. I also need to differentiate this function so I need to use a symbolic variable in it. I'm using the function in: https://www.mathworks.com/matlabcentral/fileexchange/37279-erlang-b-continuation?product=EL

However, gammainc does not accept symbolic variables, i've tried to use igamma(nu,z)/gamma(nu) for the incomplete gamma upper, the problem with this one is that once I use subs command and then vpa, it always outputs NaN,

I also try another function -> gamma_symbolic (which requires maple as symengine, now i'm using matlab R2015b that cannot change between mupad and maple anymore) https://nl.mathworks.com/matlabcentral/answers/96854-how-can-i-use-incomplete-gamma-function-gammainc-in-matlab-7-5-r2007b-to-accept-symbolic-input

Please help. I spent really a lot of time trying to fix this issue. But I still haven't solved it yet!

PS. Why does the first alternative always outputs NaN? I don't understand. For example, I do:

syms S

tes = igamma(sym(S),0.5)/gamma(sym(S))

diftes = diff(tes,S)

subs(diftes, S,6)

which outputs:

tes =

igamma(S, 1/2)/gamma(S)

diftes =

((1/2)^S*(hypergeom([S, S], [S + 1, S + 1], -1/2)/S^2 - (1/(1/2)^S*pi*(log(2) + psi(1 - S) - pi*cot(pi*(S - 1))))/(gamma(1 - S)*sin(pi*(S - 1)))) + (1/2)^S*log(1/2)*expint(1 - S, 1/2))/gamma(S) - (psi(S)*igamma(S, 1/2))/gamma(S)

ans =

NaN

Please help. It seems like I can never solve this!

[Torsten]

Plotting "diftes" should show why you can't evaluate it for S=6.

Best wishes

Torsten.

[Torsten]

By the way:

I think you mean

tes=igamma(0.5,S)/gamma(0.5),

don't you ?

Best wishes

Torsten.

[K_Kharis]

Hi Torsten,

Thanks for your message. I use sym(S) because I saw in the documentation that it is for a sym object. I did try using igamma(0.5,S)/gamma(0.5) first, but since it did output NaN, I thought this was the problem.

I tried to plot it but:

S = [0:50];
>> plot(S,diftes)
  Error using plot
  A numeric or double convertible argument is expected

I still don't get it. Is there something that I'm missing here?

[Torsten]

Please exactly tell us whether you want to analyze

igamma(0.5,S)/gamma(0.5)

or

igamma(S,0.5)/gamma(S)

Best wishes

Torsten.

[K_Kharis]

Sorry, I had a typo.

I originally need:

1/(gammainc(A,S,'upper')*x);

with A = 0.5 (given parameter). So I change it using gammainc(z, nu, 'upper') = igamma(nu, z)/gamma(nu). with:

igamma(S, 0.5)/gamma(S)

And I need S as a symbolic variable because I want to differentiate this function.

The differentiation always seems to work, but once I use subs it outputs NaN