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ON SOME RECURSION RELATIONS FOR HORN'S HYPERGEOMETRIC FUNCTIONS OF THREE VARIABLES
P. Agarwal,A. SHEHATA,S. I. MOUSTAFA,K. CHAKRABORTY 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.2
The principal aim of this paper to study the recursion formulas for the Horns hypergeometric functions of three variables. Earlier in [Shehata, A.; and Moustafa, S.I. Some new results for Horn's hypergeometric functions Γ1 and Γ2. Journal of Mathematics and Computer Science, (2021), 23 (1), 26{35.], and Pathan et al. [Pathan, M.A.; Shehata, A.; and Moustafa, S.I. Certain new formulas for the Horns hypergeometric functions. Acta Uni- versitatis Apulensis, (2020)] have studied the new results for Horns hypergeometric functions. Motivated by the above works here we will derive some contiguous relation for the families of Horn hypergeometric functions GA, GB, GC, GD and G C of three variables. After that we will establish the differential reclusion relations and differential operators for GA, GB, GC, GD and G* C of three variables, respectively.
Moustafa, Osama S.,Badr, Mahmoud Z.A.,El-Emary, Talaat I. Korean Chemical Society 2002 Bulletin of the Korean Chemical Society Vol.23 No.4
Diazotization of 3-amino-2-ethoxycarbonylthieno[2,3-b]quinoxaline 1 gave the diazonium salt 2 which was reacted with SO2 and N-methylaniline to give sulfamoylquinoxaline derivatives 3-5. Imidazothienoquinoxaline 8 was obtained from the reaction of carboxylic acid hydrazide 6 with nitrous acid and followed by boilling the carboazide 7 in dry xylene. Also, compound 6 react with CH(OEt)3 to give aminopyrimidine 9 which was reacted with arylidene malonodinitrile, furfural and/or dimethoxy-tetrahydrofuran to afford compounds 10, 11 and/or 12 respectively. Refluxing of 6 with CS2 gave oxadiazolylthienoquinoxaline 13, reaction of 13 with hyrazine hydrate, CH(OEt)3, nitrous acid, CS2 and a-halocompounds to give 14-19.