A note on an expansion of hypergeometric functions of two variables

Author:
Arun Verma

Journal:
Math. Comp. **20** (1966), 413-417

DOI:
https://doi.org/10.1090/S0025-5718-66-99930-3

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References | Additional Information

**[1]**R. P. Agarwal, "An extension of Meijer's -function,"*Proc. Nat. Inst. Sci. India Part*A, v. 32, 1965. (To appear.) MR**0204717 (34:4555)****[2]**W. N. Bailey, "Some expansions in Bessel functions involving Appell functions ,"*Quart. J. Math. Oxford Ser.*, v. 6, 1935, pp. 233-238.**[3]**T. W. Chaundy, "Expansions of hypergeometric functions,"*Quart. J. Math. Oxford Ser.*, v. 13, 1942, pp. 159-171 MR**4**, 197. MR**0007819 (4:197d)****[4]**L. Carlitz & W. A. Al-Salam, "Some functions associated with Bessel functions,"*J. Math. Mech.*, v. 12, 1963, pp. 911-933. MR**27**#4962. MR**0155020 (27:4962)****[5]**C. Fox, "The expansion of hypergeometric function in terms of similar series,"*Proc. London Math. Soc.*, v. 26, 1927, pp. 201-210.**[6]**J. L. Fields & Jet Wimp, "Expansions of hypergeometric functions in hypergeometric functions,"*Math. Comp.*, v. 15, 1961, pp. 390-396. MR**23**#A3289. MR**0125992 (23:A3289)****[7]**C. S. Meijer, "Expansion theorems for the -function," a) I, II,*Nederl. Akad. Wetensch. Proc. Ser.*A, v.*Indag. Math.*, v. 14, 1952, pp. 369- 379, 483-487. MR**14**, 469, 642; b) III, IV, V,*Nederl. Akad. Wetensch. Proc. Ser.*A, v.*Indag. Math.*, v. 15, 1953, pp. 43-49, 187-193, 349-357. MR**14**, 748, 979; MR**15**, 422; c) ibid., VI, VII, VIII,*Nederl. Akad. Wetensch. Proc. Ser.*A, v.*Indag. Math.*, v. 16, 1954, pp. 77-82, 83-91, 273-279. MR**15**, 791, 955; d) ibid., IX, X,*Nederl. Akad. Wetensch. Proc. Ser.*A, v.*Indag. Math.*, v. 17, 1955, pp. 243-251, 309-314. MR**16**, 1106; e) ibid., XI,*Nederl. Akad. Wetensch. Proc. Ser.*A, v.*Indag. Math.*, v. 18, 1956, pp. 70-82. MR**17**, 846. MR**0051373 (14:469e)****[8]**S. O. Rice, "On contour integrals for the product of Bessel functions,"*Quart. J. Math. Oxford Ser.*, v. 6, 1935, pp. 52-64.**[9]**H. M. Srivastava, "Some expansions in product of hypergeometric functions,"*Proc. Cambridge Philos. Soc.*, v. 62, 1965. MR**0188501 (32:5939)****[10]**A. Verma, "A class of expansions of -functions and the Laplace transform,"*Math. Comp.*, v. 19, 1965, pp. 661-664.**[11]**A. Verma, "Certain expansions involving generalised basic hypergeometric series,"*Math. Comp.*, v. 20, 1966, pp. 151-157.**[12]**A. Verma, "Expansions of hypergeometric functions of two variables,"*Collect. Math.*(To appear.)**[13]**Jet Wimp & Y. L. Luke, "Expansion formulas for generalised hypergeometric functions,"*Rend. Circ. Mat. Palermo*, (2), v. 11, 1962, pp. 351-366. MR**0166405 (29:3681)**

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-66-99930-3

Article copyright:
© Copyright 1966
American Mathematical Society