The Lommel polynomials and related formulas (Q6649823)

The purpose of this article is to present and/or prove formulas for Lommel polynomials. These polynomials satisfy the same recurrence as Bessel functions. So far, Bessel functions have found more applications than Lommel polynomials. \N\NSome observations: \NThere is no need to write limit in the elementary formula after formula (1.1). The formulas in [\textit{G. N. Watson}, A treatise on the theory of Bessel functions. 2nd ed. Cambridge: Cambridge Univ. Press (1995; Zbl 0849.33001)] can also be found in [\textit{A. Erdélyi} et al., Higher transcendental functions. Vol. II. Bateman Manuscript Project. New York-Toronto-London: McGraw-Hill Book Co (1953; Zbl 0052.29502)]. One should prove new formulas for special functions, and number them. Especially when some of them are false, like the two formulas after formula (2.1). The function csc on page 706 means the reciprocal of the sine function. The function arguments for hypergeometric series on various places are placed where there is extra space for the parameters. The author has copied the formula [\textit{Yu. A. Brychkov} and \textit{N. Saad}, Integral Transforms Spec. Funct. 25, No. 2, 111--123 (2014; Zbl 1282.33020); (39)] which should state Re\((c')>0\), since infinity of Gamma functions in denominators just gives result zero. The title [\textit{Yu. A. Brychkov} and \textit{N. Saad}, Integral Transforms Spec. Funct. 25, No. 2, 111--123 (2014; Zbl 1282.33020)] should also be changed. It is not clear which formulas are used to prove formulas (7.3) and (7.4) and the formulas on page 712. Certainly, more formulas of this type could be obtained. A most interesting paper.