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DECOMPOSITION FORMULAS FOR THE GENERALIZID HYPERGEOMETRIC 4F3 FUNCTION
HASANOV ANVARDJAN,최준상,TURAEV MAMASALI 호남수학회 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 in-volving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric 4F3 function are then given. Fur-thermore, the integral representations associated with generalized hypergeometric functions are also presented.
SOME DECOMPOSITION FORMULAS ASSOCIATED WITH THE SARAN FUNCTION FE
김용섭,HASANOV ANVARDJAN,이창현 호남수학회 2010 호남수학학술지 Vol.32 No.4
With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy,the authors investigate decomposition formulas associated with Saran's function FE in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this pur-pose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function FE.
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.
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.