I have been working on a lengthy math expression and finally I simplified it as $\sum_{t=0}^T C_t^{T}(-1)^t\Gamma(1+t/\beta_A)$ where $C_t^{T}$ is $T!/(T-t)!t!$
The problem is, I have to validate this expression by using fractional experimental results, i.e $T$ must be fractional. However, none of the math programs count the above expression correctly when $T$ is not integer.
What can I do? Thank you very much for your helps.
Your model is inherently time-discrete by design, so thinking of fractional times seems a nonsense.
Maybe you can switch to a continuous time description, where the summation would turn to an integration, but with the little information given, I can't say more.