en عمومى General پژوهشي Research paper <div style="text-align: justify;">Many works are elaborated to derive interesting identities for hypergeometric-type series containing as a factor a digamma function. In the present paper, new reduction formulae for Kamp&eacute; de F&eacute;riet series of types F_2:1;0 ^1:2;1 and F_3:1;0 ^2:2;1 are performed. By specializing certain parameters, series identities and related reduction identities are deduced. An interesting application is also studied concerning the evaluation of the average intensity of a multi-Gaussian beam propagating through a turbulent atmosphere.</div> Generalized hypergeometric function, Kampé de Fériet function, Incomplete gamma functions, Hyperbolic sine and cosine integral functions. 161 172 http://ijmsi.ir/browse.php?a_code=A-10-4989-1&slc_lang=en&sid=1 Abdelmajid Belafhal belafhal@gmail.com 100319475328460012040 100319475328460012040 No LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua¨ıb Doukkali University, P. B 20, 24000 El Jadida, Morocco El Mostafa El Halba elhalbams@gmail.com 100319475328460012041 100319475328460012041 No LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua¨ıb Doukkali University, P. B 20, 24000 El Jadida, Morocco Talha Usman talhausman.maths@gmail.com 100319475328460012042 100319475328460012042 Yes Preparatory Studies Center, Mathematics and Computing Skills Unit, University of Technology and Applied Sciences, P.O. Box: 484, P.C: 411, Sur, Oman