Unified fractional \(q\)-integral operator of \(q\)-special functions (Q2906978)

A \(q\)-analogue of the Fox H-function is introduced in the spirit of an earlier paper from 1983. The author should show that this \(q\)-analogue approaches the Fox H-function from [\textit{H. M. Srivastava, K. C. Gupta} and \textit{S. P. Goyal}, The H-functions of one and two variables with applications. New Delhi-Madras: South Asian Publishers (1982; Zbl 0506.33007)] when \(q\to 1\), however, she did not do this. Several special cases are shown in Table 1, but that there are many \(q\)-trigonometric and \(q\)-hyperbolic functions in the literature is not mentioned. The \(q\)-gamma function is defined on page 188 and not used in Definition (27), p. 191 (cf. [\textit{Nguyen Xuan Thao}, Russ. Math. 45, No. 2, 68--70 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 2, 73--75 (2001; Zbl 1011.33013), p. 68]). NEWLINENEWLINENEWLINE NEWLINEReviewer's remark: It is not clear which q-trigonometric functions are used in the end. Several of the elementary formulas in the beginning could be skipped.