On partial derivatives of the incomplete beta function

Some results on the q-Beta function

“…Finally, we note that all results obtained in the paper are in agreement with the results given in [5][6][7][8][9][10] as q tends 1.…”

Some results on the beta function and the incomplete beta function

“…We first consider the integral For further results on the Beta function and the incomplete Beta function, see [3][4][5][6].…”

On defining the q-beta function for negative integers

“…Fisher at al. used neutrices to define the gamma and beta function for all real values [4,5].Özçaḡ et al applied the neutrix limit to extend the definition of the incomplete beta function and its partial derivatives to negative integers, [11,12]. It was shown that the neutrix limit of the q-gamma function and its partial derivatives exist for all values, [13].…”