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ON SEVERAL NEW CONTIGUOUS FUNCTION RELATIONS FOR k-HYPERGEOMETRIC FUNCTION WITH TWO PARAMETERS
Chinra, Sivamani,Kamalappan, Vilfred,Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3
Very recently, Mubeen, et al. [6] have obtained fifteen contiguous function relations for k-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for k-hypergeometric functions with two parameters. Obviously, for $k{\rightarrow}1$ we recover the results obtained by Cho, et al. [2] and Rakha, et al. [8].
D. Narendar,N. Arjun,K. Someshwar,Y. Madhusudan Rao 한국약제학회 2016 Journal of Pharmaceutical Investigation Vol.46 No.3
The aim of the investigation was to develop and optimize the effervescent floating matrix tablets of Quetiapine Fumarate (QF) by using 23 factorial design. Amount of hydroxyl propyl methyl cellulose K4M (HPMC K4M (A1)), amount of hydroxyl propyl methyl cellulose K15M (HPMC K15M (A2)) and amount of sodium bicarbonate (A3) (as gas-generating agent) were considered as independent variables and floating lag time (FLT, B1) (sec), percent drug release in 2 h (B2, Q2) and 6 h (B3, Q6) as dependent variables, respectively. Floating tablets of QF were prepared by effervescent technique using direct compression method. Drug-excipient compatibility studies were conducted by using DSC and FTIR techniques. The floating tablets were evaluated for physical characteristics, drug content, swelling index, in vitro buoyancy and in vitro release studies. Optimized formulation contains 25 mg of A1, 12.5 mg of A2 and 25 mg of A3 which resulted in 32 s of B1, 32.89 ± 3.1 % of B2, and 73.61 ± 1.8 % of B3, respectively. DSC and FTIR studies revealed that no interaction between the drug and excipients in the developed formulation. The drug release followed Higuchi model and the Fickian transport. Physico-chemical stability studies revealed that the optimized formulation was stable for 90 days. Based on the physical evaluation and in vitro drug release characteristics, it was concluded that QF was suitable for incorporation into a floating drug delivery system.
Certain summation formulas due to Ramanujan and their generalizations
Arjun K. Rathie,Shaloo Malani,Rachana Mathur,최준상 대한수학회 2005 대한수학회보 Vol.42 No.3
The authors aim at deriving four generalized summationformulas, which, upon specializing their parameters, give manysummation identities including, especially, the four veryinteresting summation formulas due to Ramanujan. The results arederived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.
Generalization of Whipple's theorem for double series
Arjun K. Rathie,Vimal K. Gaur,Yong Sup Kim,Chan Bong Park 호남수학회 2004 호남수학학술지 Vol.26 No.1
In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theo- rem on the sum of a 3F2. The aim of this paper is to derive twenty 칥e results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty 칥e summation for- mulas closely related to the Watson's theorem on the sum of a 3F2 obtained recently by Lavoie, Grondin, and Rathie.
( K. Shani ),( Junesang Choi ),( Arjun K. Rathie ) 호남수학회 2016 호남수학학술지 Vol.38 No.4
The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kum- mer using a differential equation approach.
A NOTE ON GENERALIZATIONS OF PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS
Rathie, Arjun K.,Choi, June-Sang Korean Mathematical Society 1998 대한수학회보 Vol.35 No.2
The aim of this paper is to establish generalizations of the well known Preece's identity and other identities involving product of generalized hypergeometric series by using new and very short method.
GENERALIZATION OF WHIPPLE'S THEOREM FOR DOUBLE SERIES
RATHIE, ARJUN K.,GAUR, VIMAL K.,KIM, YONG SUP,PARK, CHAN BONG The Honam Mathematical Society 2004 호남수학학술지 Vol.26 No.1
In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty five results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty five summation formulas closely related to the Watson's theorem on the sum of a $_3F_2$ obtained recently by Lavoie, Grondin, and Rathie.
CERTAIN SUMMATION FORMULAS DUE TO RAMANUJAN AND THEIR GENERALIZATIONS
RATHIE ARJUN K.,MALANI SHALOO,MATHUR RACHANA,CHOI JUNESANG Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
The authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan. The results are derived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.