Some Transformation of a Multiple Hypergeometric Series of Lauricella Function of n Variables
Some Transformation of a Multiple Hypergeometric Series of Lauricella Function of n Variables
摘要
This paper deals with an integral transformation involving Whittaker function Mk,m(X) into a multiple hypergeometric series of Lauricella function FA(n) of n variables. A number of known and new transformation and reduction formulae for a hypergeometric function 2F1, Appell function F2, Lauricella function FA(3) and a hypergeometric function of four variables Fp(4) are derived as special cases.
参考文献10
-
1Lauricella, G. 1893. "Sulle Funzioni Ipergeometriche a Piu Variabili." Rend. Circ. Mat. Palermo 7: I 11-158.
-
2Srivastava, H. M., and Manocha, H. L. 1984. A Treatiseon Generating Functions. Halsted Press (Ellis Horwood Limited, Chichester): 3ohn Wiley and sons, New York.
-
3Pathan, M. A. 1979. "On a Transformation of a General Hypergeometric Series of Four Variables." Nederl, Akad. Wetensch. Proc Ser. A. 82=Indag Math 4._A_l, New York, 171-5.
-
4Whittaker, E. T. 1903. "An Expression of Certain Known Function as Generalized Hypergeometric Functions." Bull. Amer. Math. Soc. 10: 125-134.
-
5Whittaker, E. T., and Watson, G. N. 1990. A Course of Modern Analysis, 4th ed. Cambridge, England.Cambridge University.
-
6Erdelyi, A., 1954. "Table of integral transforms." Vol.l, McGraw-HilL New York.
-
7Erdelyi, A. 1948. "Transformation of Hypergeometric Functions of Two Variables." proc. Roy, Soc. Edinburgh Sect. A 62: 378-385.
-
8Khan, B., and Pathan, M. A. 1982. "Some Transformations of Appell's Function F4." Tamkang J. Math. 13 (1): 25-35.
-
9Srivastav, H. M., and Karlsson, P. W. 1985. Multiple Gaussian Hypergeometric Series. Halsted Press (Ellis Horwood Limited, Chichester): John Wiley and sons, New York, Chichester Brisbane, Toronto.
-
10Srivastav, H. M., and Panda, R. 1976. "An Integral Representation for the Product of Two Jacobi Polynomials." J. London Math. Soc. 12 (2): 419-425.
-
1梁小林,牛彩云,田学.更新几何过程及相关性质[J].应用概率统计,2015,31(4):384-394. 被引量:2
-
2周银海.关于几何凸函数的几个结果[J].湖州师范学院学报,2006,28(1):54-56. 被引量:3
-
3赵燕红.微分从属与几何函数理论的研究[J].数学学习与研究,2012(19):3-3.
-
4Xiao Xia WANG.New Proof for Some Terminating Hypergeometric Series Identities[J].Journal of Mathematical Research and Exposition,2011,31(1):115-122.
-
5杨智文.关于k极计算[J].广西教育学院学报,1998(B07):176-186.
-
6罗睿,黄晓明,张晓萌.沥青层底裂缝几何函数和权函数分析[J].西南交通大学学报,2002,37(4):387-392. 被引量:1
-
7殷慰萍,王安,赵晓霞.第一类超Cartan域上的比较定理[J].中国科学(A辑),2000,30(11):990-1001. 被引量:8
-
8朱尧辰.几何过程及其应用[J].国外科技新书评介,2008(3):7-7.
-
9袁平之.关于丢番图方程X^2+4P^m-1=4P^n[J].铁道科学与工程学报,1989(3):85-92. 被引量:1
-
10Yang Zhang Hai-Xing Miao.Nonlinear density fluctuation field theory for large scale structure[J].Chinese Journal of Astronomy and Astrophysics,2009,9(5):501-508.