On certain new formulas for the Horn’s hypergeometric functions $${\mathcal {G}}_{1}$$, $${\mathcal {G}}_{2}$$ and $${\mathcal {G}}_{3}$$

Inspired by the recent work Sahin and Agha gave recursion formulas for $${\mathcal {G}}_{1}$$ {G}}_{2}$$ Horn hypergeometric functions (Sahin in Miskolc Math Notes 16(2):1153–1162, 2015). The object of is to establish several new relations, relevant differential formulas, integral operators, infinite summations interesting results Horn’s , {G}}_{3}$$ .