By Dikran Dikranjan, Luigi Salce

Includes a stimulating collection of papers on abelian teams, commutative and noncommutative earrings and their modules, and topological teams. Investigates presently well known subject matters similar to Butler teams and nearly thoroughly decomposable teams.

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1) are related in the following way : (β)n Mn (x; β, c) = Pn(β−1,−n−β−x) n! 2−c c . 1) in the following way : p Kn (x; p, N ) = Mn x; −N, . p−1 References. [6], [10], [13], [19], [21], [31], [32], [39], [43], [50], [52], [64], [67], [69], [80], [104], [123], [130], [154], [170], [172], [173], [181], [183], [212], [222], [227], [233], [239], [247], [250], [274], [286], [287], [296], [298], [301], [307], [316], [323], [338], [391], [394], [407], [409]. 10 Krawtchouk Definition. Kn (x; p, N ) = 2 F1 −n, −x 1 −N p , n = 0, 1, 2, .

N n! References. [6], [10], [13], [19], [21], [31], [32], [39], [50], [64], [67], [81], [123], [124], [142], [154], [181], [183], [212], [222], [274], [286], [287], [288], [294], [296], [298], [301], [307], [316], [323], [388], [394], [407], [409]. 13 Hermite Definition. Hn (x) = (2x)n 2 F0 Orthogonality. −n/2, −(n − 1)/2 1 − 2 − x . 1) ∞ 1 √ π 2 e−x Hm (x)Hn (x)dx = 2n n! δmn . 2) −∞ Recurrence relation. Hn+1 (x) − 2xHn (x) + 2nHn−1 (x) = 0. 3) Normalized recurrence relation. 4) where Hn (x) = 2n pn (x).

41) or equivalently d 1 − x2 dx Rodrigues-type formulas. 1 2 Un (x) = −(n + 1) 1 − x2 1 (1 − x2 )− 2 Tn (x) = 1 (1 − x2 ) 2 Un (x) = (−1)n ( 12 )n 2n d dx (n + 1)(−1)n ( 32 )n 2n Generating functions. − 12 Tn+1 (x). 42) n d dx 1 (1 − x2 )n− 2 . 43) n 1 (1 − x2 )n+ 2 . 44) ∞ 1 − xt = Tn (x)tn . 45) ∞ R − (x − 1)t 1 2 2 0 F1 γ, −γ 1 − R − t 1 2 2 ∞ − (x + 1)t 1 2 2 0 F1 2 F1 = n=0 1 − 2xt + t2 . 46) Tn (x) n t . 1 2 n n! 47) ∞ − (x2 − 1)t2 1 4 2 ext 0 F1 2 F1 1 1 2 n (1 + R − xt) = Tn (x)tn , R = 2 n!