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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.
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.
Elgun E. Hasanov,Ravan A. Rahimov,Yusif Abdullayev,Ziyafaddin H. Asadov,Gulnara A. Ahmadova,Aygun M. Isayeva,Saida F. Ahmadbayova,Fedor I. Zubkov,Jochen Autschbach 한국공업화학회 2020 Journal of Industrial and Engineering Chemistry Vol.86 No.-
Six cocogem surfactants were synthesized from N,N,Nʹ,Nʹ-tetra-(propane-2-olyl)-1,6-hexanediamine andhigher monocarboxylic acids: capric, lauric, myristic, palmitic, stearic and oleic. N,N,Nʹ,Nʹ-tetra-(propane-2-olyl)-1,6-hexanediamine was synthesized from hexamethylenediamine and propylene oxide at roomtemperature, without utilizing any catalyst or solvent. Surface tension, conductivity, foaming ability,foam stability, emulsion stability, viscosity and density measurements were performed on aqueoussolutions of all cocogem surfactants. Their surface activity and colloidal-chemical parameters such ascritical micelle concentration (CMC), surface pressure at CMC (pCMC), surface tension at CMC (gCMC),surface excess (Gmax), concentration required for 20 mN/m reduction of surface tension (C20), Gibbsenergies of adsorption and micellization (DGad and DGmic) were recorded and variation of theseparameters based on hydrophobic chain length and structure was investigated experimentally andcomputationally. Synthesized surfactants with myristic, palmitic, and stearic tail continued to decreasesurface tension even above CMC. The possible reason of this unusual behavior was determined based oncomputational studies. Surface activity parameters of cocogem surfactant with oleic tail disobeyed thegeneral tendency established by other cocogems with saturated tail group. Palmitic and stearic acid basedcocogem surfactants had good foam stability and the reason of this high foam stability was rationalizedwith high viscosity of their solutions.
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.
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.
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.
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.
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.
INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION H<sub>C</sub>
Choi, Junesang,Hasanov, Anvar,Turaev, Mamasali The Honam Mathematical Society 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 $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding 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 $H_C$.