Integral representations for the Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, and the generalized Bessel polynomials

Russian Journal of Mathematical Physics - Tập 19 Số 1 - Trang 121-130 - 2012
H. M. Srivástava1, Shy‐Der Lin2, Shuoh-Jung Liu2, Han-Chun Lu3
1Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V 8W 3R4, Canada
2Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, 32023, Taiwan, Republic of China
3Department of Mathematics, Tamkang University, Tamsui, 25137, Taiwan, Republic of China

Tóm tắt

Từ khóa


Tài liệu tham khảo

W. A. Al-Salam, “The Bessel Polynomials,” Duke Math. J. 24, 529–545 (1957).

S. K. Chatterjea, “Some Generating Functions,” Duke Math. J. 32, 563–564 (1965).

A. Erdélyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Higher Transcendental Functions, Vol. I (McGraw-Hill Book Company, New York, Toronto and London, 1953).

A. Erdélyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Higher Transcendental Functions, Vol. III (McGraw-Hill Book Company, New York, Toronto and London, 1953).

B. González, J. Matera, and H. M. Srivastava, “Some q-Generating Functions and Associated Generalized Hypergeometric Polynomials,” Math. Comput. Modelling 34(1/2), 133–175 (2001).

E. Grosswald, Bessel Polynomials, Lecture Notes in Mathematics, Vol. 698 (Springer-Verlag, Berlin, Heidelberg and New York, 1978).

H. L. Krall and O. Frink, “A New Class of Orthogonal Polynomials: The Bessel Polynomials,” Trans. Amer. Math. Soc. 65, 100–115 (1949).

S.-D. Lin, Y.-S. Chao, and H. M. Srivastava, “Some Families of Hypergeometric Polynomials and Associated Integral Representations,” J. Math. Anal. Appl. 294, 399–411 (2004).

S.-D. Lin, H. M. Srivastava, and P.-Y. Wang, “Some Families of Hypergeometric Transformations and Generating Relations,” Math. Comput. Modelling 36, 445–459 (2002).

S.-D. Lin, S.-J. Liu, and H. M. Srivastava, “Some Families of Hypergeometric au]Polynomials and Associated Multiple Integral Representations,” Integral Transforms Spec. Funct. 22, 403–414 (2011).

S.-D. Lin, S.-J. Liu, H.-C. Lu, and H. M. Srivastava, “Integral Representations for the Generalized Bedient Polynomials and the Generalized Cesàro Polynomials,” Appl. Math. Comput. 218, 1330–1341 (2011).

S.-D. Lin, S.-T. Tu and H. M. Srivastava, “Some Generating Functions Involving the Stirling Numbers of the Second Kind,” Rend. Sem. Mat. Univ. Politec. Torino 59, 199–224 (2001).

S.-J. Liu, C.-J. Chyan, H.-C. Lu, and H. M. Srivastava, “Multiple Integral Representations for Some Families of Hypergeometric and Other Polynomials,” Math. Comput. Modelling 54, 1420–1427 (2011).

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Die Grundlehren der Mathematischen Wissenenschaften in Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete, Band 52, Third enlarged ed. (Springer-Verlag, Berlin-Heidelberg-New York, 1966).

E. D. Rainville, Special Functions (Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971).

H. M. Srivastava, “A Contour Integral Involving Fox’s H-Function,” Indian J. Math. 14, 1–6 (1972).

H. M. Srivastava, “Some Orthogonal Polynomials Representing the Energy Spectral Functions for a Family of Isotropic Turbulence Fields,” Z. Angew. Math. Mech. 64, 255–257 (1984).

H. M. Srivastava, “Some Integral Representations for the Jacobi and Related Hypergeometric Polynomials,” Rev. Acad. Canaria Cienc. 14, 25–34 (2002).

H. M. Srivastava and C. M. Joshi, “Integral Representation for the Product of a Class of Generalized Hypergeometric Polynomials,” Acad. Roy. Belg. Bull. Cl. Sci. (5) 60, 919–926 (1974).

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Ltd., Chichester) (John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984).

H. M. Srivastava, M. A. Özarslan, and C. Kaanoglu, “Some Families of Generating Functions for a Certain Class of Three-Variable Polynomials,” Integral Transforms Spec. Funct. 21, 885–896 (2010).

H. M. Srivastava and R. Panda, “An Integral Representation for the Product of Two Jacobi Polynomials,” J. London Math. Soc. (2) 12, 419–425 (1976).

G. Szegö, Orthogonal Polynomials, Fourth ed., American Mathematical Society Colloquium Publications, Vol. 23 (American Mathematical Society, Providence, Rhode Island, 1975).

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions, Fourth ed. (Cambridge University Press, Cambridge, London and New York, 1927).