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DECOMPOSITION FORMULAS FOR THE GENERALIZID HYPERGEOMETRIC <sub>4</sub>F<sub>3</sub> FUNCTION
Hasanov, Anvar,Turaev, Mamasali,Choi, June-Sang The Honam Mathematical Society 2010 호남수학학술지 Vol.32 No.1
By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities involving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric $_4F_3$ function are then given. Furthermore, the integral representations associated with generalized hypergeometric functions are also presented.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5
최준상,HASANOV ANVARDJAN,TURAEV MAMASALI 호남수학회 2010 호남수학학술지 Vol.32 No.3
Exton introduced 20 distinct triple hypergeometric func-tions whose names are Xi (i = 1,..., 20) to investigate their twenty Laplace integral representations whose kernels include the conflu-ent hypergeometric functions 0F1, 1F1, a Humbert function ψ2, a Humbert function Φ2. The object of this paper is to present 25 (pre-sumably new) integral representations of Euler types for the Exton hypergeometric function X5 among his twenty Xi (i = 1,..., 20),whose kernels include the Exton function X5 itself, the Exton func-tion X6, the Horn's functions H3 and H4, and the hypergeometric function F = 2F1.
FUNCTIONAL RELATIONS INVOLVING SRIVASTAVA S HYPERGEOMETRIC FUNCTIONS HB AND F(3)
Junesang Choi,Anvar Hasanov,Mamasali Turaev 충청수학회 2011 충청수학회지 Vol.24 No.2
B. C. Carlson [Some extensions of Lardner s relations between 0F3 and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232{242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some ear- lier results. Here, by simply splitting Srivastava s hypergeometric function HB into eight parts, we show how some useful and gener- alized relations between Srivastava s hypergeometric functions HB and F(3) can be obtained. These main results are shown to be spe- cialized to yield certain relations between functions 0F1, 1F1, 0F3,ª2, and their products including di??erent combinations with dif- ferent values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ª2 function and Kamp¶e de F¶eriet function, and between the product of expo- nential and Bessel functions with Kamp¶e de F¶eriet functions.
Several Integral Representations Involving Triple Hypergeometric Functions
( Junesang Choi ),( Anvar Hasanov ),( Mamasali Turaev ) 호남수학회 2011 호남수학학술지 Vol.33 No.2
A (presumably) new class of generalized triple hyper-geometric functions is presented. We also give integral representa-tions of Laplace type for certain special cases of the new class offunctions.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X2
최준상,HASANOV ANVARDJAN,TURAEV MAMASALI 한국수학교육학회 2010 純粹 및 應用數學 Vol.17 No.4
Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113{119] introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1, . . . , 20) to investigate their twenty Laplace integral representations whose kernels include the con°uent hypergeometric functions ₀F₁,₁F₁, a Humbert functionΨ2, a Humbert function Φ2. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function X₂ among his twenty Xi (i = 1, . . . , 20), whose kernels include the Exton function X₂ itself, the Appell function F₄and the Lauricella function FC.
INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION H_C
최준상,Anvar Hasanov,Mamasali Turaev 호남수학회 2012 호남수학학술지 Vol.34 No.4
While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeo-metric series of the second order, which were denoted by HA, HB and HC. Each of these three triple hypergeometric functions HA,HB and HC has been investigated extensively in many di erent ways including, for example, in the problem of nding their inte-gral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function HC.
Decomposition formulas and integral representations for some Exton hypergeometric functions
Junesang Choi,Anvar Hasanov,Mamasali Turaev 충청수학회 2011 충청수학회지 Vol.24 No.4
Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions F_3 and F_4, Horn's functions H_3 and H_4, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions X_i (i=6, 8, 14)each of whose kernels contains the Horn's function H_4.
DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS
Junesang Choi,Anvar Hasanov,Mamasali Turaev 충청수학회 2012 충청수학회지 Vol.25 No.4
Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell s functions F3 and F4, Horn s functions H3 and H4, and Gauss s hypergeometric function F. We also give some integral representa- tions for the Exton functions Xi (i = 6; 8; 14) each of whose kernels contains the Horn s function H4.
INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB
최준상,Anvar Hasanov,Mamasali Turaev 한국수학교육학회 2012 純粹 및 應用數學 Vol.19 No.2
While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by HA, HB and HC. Each of these three triple hypergeometric functions HA, HB and HC has been investigated extensively in many di®erent ways including,for example, in the problem of ¯nding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function HB.