I know about the usual notation for referring to hypergeometric functions, such as $_pF_q$.
However, I've found something like $\boxed{_p\tilde{F}_q}$ as a part of the expression for calculating the raw moments of a random variable following a doubly noncentral $F$ distribution in this web page: http://mathworld.wolfram.com/NoncentralF-Distribution.html . I had never seen that before.
What does $_p\tilde{F}_q$ stand for?
As I noted in the comments, the function they neglected to define in the MathWorld link is what they term the "regularized hypergeometric function",
$${}_p \tilde{F}_q\left({{a_1,\dots,a_p}\atop{b_1,\dots,b_q}}\middle|x\right)=\frac1{\prod\limits_{k=1}^q\Gamma(b_k)}{}_p F_q\left({{a_1,\dots,a_p}\atop{b_1,\dots,b_q}}\middle|x\right)$$
i.e., the usual hypergeometric function divided by the product of gamma functions evaluated at the denominator parameters.
In the DLMF, the term "scaled" or "Olver's hypergeometric function" is used, with the notation ${}_p\mathbf{F}_q\left(\mathbf a;\mathbf b;z\right)$.