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Qureshi, I.; Quraishi, K. A.; Khan, B.; Arora, A.

Transformations associated with quadruple hypergeometric functions of Exton and Srivastava. (English) Zbl 1364.33007

Asia Pac. J. Math. 4, No. 1, 38-48 (2017).
Summary: In this paper, we obtain some new transformations relating quadruple hypergeometric function \(F^{(4)}\) of Srivastava and quadruple hypergeometric functions \(D_5\), \(K_{12}\), \(K_{13}\) of Exton. Two correct forms of an erroneous transformation of Exton are also given.

Cited in 2 Documents

MSC:

33C05 Classical hypergeometric functions, \({}_2F_1\)
33C65 Appell, Horn and Lauricella functions
33C70 Other hypergeometric functions and integrals in several variables

Keywords:

Pochhammer’s symbol; quadruple hypergeometric functions of Exton and Srivastava; hypergeometric transformations; series iteration technique
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References:

[1] Carlson, B. C.; Lauricella’s Hypergeometric Function \(F_D\). J. Math. Anal. Appl., 7 (1963), 452-470. · Zbl 0122.06704
[2] Chandel, R. C. S.; On Some Multiple Hypergeometric Functions Related to Lauricella Functions, \(J\tilden\baran\barabha~Sect.~A, 3 (1973), 119-136\). · Zbl 0288.33012
[3] Chandel, R. C. S.; Errata and Addenda To: On Some Multiple Hypergeometric Functions Related to Lauricella Functions, \(J\tilden\baran\barabha~Sect.~A, 5(1975), 177-180\). · Zbl 0346.33003
[4] Chandel, R. C. S. and Gupta, A. K.; Multiple Hypergeometric Functions Related to Lauricella’s Functions, \(J\tilden\baran\barabha~Sect.~A, 16(1986), 195-210\). · Zbl 0615.33001
[5] Exton, H.; On Certain Confluent Hypergeometric Functions of Three Variables, Ganita, 21(2)(1970), 79-92. · Zbl 0222.33007
[6] Exton, H.; On Two Multiple Hypergeometric Functions Related to Lauricella’s \(F^(n)_D, J\tilden\baran\barabha~Sect.~A, 2(1972), 59-73\). · Zbl 0288.33011
[7] Exton, H.; Certain Hypergeometric Functions of Four Variables. Bull. Soc. Math. Gr \(\acute\texte\) ce (N.S.), 13(1972), 104-113. · Zbl 0259.33005
[8] Exton, H.; Some Integral Representations and Transformations of Hypergeometric Functions of Four Variables, Bull. Soc. Math. Gr \(\acute\texte\) ce (N.S.), 14(1973), 132-140. · Zbl 0278.33005
[9] Exton, H.; On a Certain Hypergeometric Differential System-I, Funkcial Ekvac., 14(1971), 79-87; Corrigendum. Ibid., 16 (1973), 69. · Zbl 0219.33002
[10] Exton, H.; On a Certain Hypergeometric Differential System-II, Funkcial Ekvac., 16(1973), 189-194. · Zbl 0286.33006
[11] Exton, H.; On Certain Confluent Hypergeometric Functions of Four Variables. Ganita, 25(2)(1974), 23-46. · Zbl 0343.33001
[12] Exton, H.; Multiple Hypergeometric Functions and Applications, Halsted Press(Ellis Horwood Ltd., Chichester, U. K.), John Wiley and Sons, New York, Chichester, 1976. · Zbl 0337.33001
[13] Jain, R. N.; The Confluent Hypergeometric Functions of Three Variables, Proc. Nat. Acad. Sci. India, Sect. A, 36(1966), 395-408. · Zbl 0259.33003
[14] Karlsson, P. W.; Reduction of Certain Generalized Kamp \(\acute\texte\) de \(F \acute\texte\) riet Functions, Math. Scand., 32(1973), 265-268. · Zbl 0268.33006
[15] Karlsson, P. W.; On Intermediate Lauricella’s Functions, J\=n\=an\=abha, Sect. A, 16(1986), 211-222. · Zbl 0615.33003
[16] Lauricella, G.; Sulle Funzioni Ipergeometriche a Pi \(\acute\textu\) Variabili, Rend. Circ. Mat. Palermo, 7(1893), 111-158. · JFM 25.0756.01
[17] Pandey, R. C.; On Certain Hypergeometric Transformations, J. Math. and Mach., 12(1)(1963), 113-118. · Zbl 0112.04602
[18] Qureshi, M. I. and Pathan, M. A.; A Note on the Sum of Appell Function \(F_2\), Indian J. Pure Appl. Math., 15(11)(1984), 1239-1243. · Zbl 0573.33005
[19] Rainville, E. D.; Special Functions, The Macmillan Co. Inc., New York 1960; Reprinted by Chelsea Publ. Co. Bronx, New York, 1971. · Zbl 0092.06503
[20] Saran, S.; Hypergeometric Functions of Three Variables. Ganita, 5(2)(1954), 77-91; Corrigendum. Idid., 7 (1956), 65. · Zbl 0058.29602
[21] Saran, S.; Transformations of Certain Hypergeometric Functions of Three Variables, Acta. Math., 93(1955), 293-312. · Zbl 0064.30902
[22] Srivastava, H. M.; Infinite Series of Certain Products Involving Appell’s Double Hypergeometric Functions-I, Glasnik Mat. Ser. III, 4(24)(1969), 67-73. · Zbl 0176.01802
[23] Srivastava, H. M.; A Formal Extension of Certain Generating Functions-I, Glasnik Mat. Ser. III, 5(25)(1970), 229-239. · Zbl 0192.41401
[24] Srivastava, H. M.; A Formal Extension of Certain Generating Functions II, Glasnik Mat. Ser. III, 6(26) (1971), 35-44. · Zbl 0204.38402
[25] Srivastava, H. M. and Manocha, H. L.; A Treatise on Generating Functions, Halsted Press(Ellis Horwood, Chichester, U.K.) John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984. · Zbl 0535.33001
[26] Srivastava, H. M. and Panda, R.; An Integral Representation for the Product of Two Jacobi Polynomials, J.London Math. Soc., 2(12), (1976), 419-425. · Zbl 0304.33015
[27] Srivastava, H. M. and Pathan, M. A.; Some Bilateral Generating Functions for the Extended Jacobi Polynomial-I, Comment. Math. Uni. St. Paul., 28(1), (1979), 23-30. · Zbl 0415.33001
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