Home

# Double Meijer transformations of certain hypergeometric functions

## Extract

Following the usual notation for generalized hypergeometric functions we let

(a) denotes the sequence of A parameters

that is, there are A of the a parameters and B of the b parameters. Thus ((a))m has the interpretation

with a similar interpretation for ((b))m; Δ(k; α) stands for the set of k parameters

and for the sake of brevity, the pair of parameters like α + β, α − β will be written as α ± β, the gamma product Γ(α + β) Γ(α − β) as Γ(α ± β), and so on.

## References

Hide All
(1)Abdul-Halim, N. and Al-Salam, W. A.Double Euler transformations of certain hypergeometric functions. Duke Math. J. 30 (1963), 5162.
(2)Al-Salam, W. A.The Bessel polynomials. Duke Math. J. 24 (1957), 529547.
(3)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. I (McGraw-Hill; New York, 1953).
(4)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. II (McGraw-Hill; New York, 1953).
(5)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. II (McGraw-Hill; New York, 1955).
(6)Krall, H. L. and Frink, O.A new class of orthogonal polynomials: the Bessel polynomials. Trans. Amer. Math. Soc. 65 (1949), 100115.
(7)Rainville, E. D.Special functions (Macmillan; New York, 1960).
(8)Singh, R. P.A note on double transformations of certain hypergeometric functions. Proc. Edinburgh Math. Soc. (2), 14 (1965), 221227.
(9)Slater, L. J.Confluent hypergeometric functions (Cambridge, 1960).
(10)Slater, L. J.Generalized hypergeometric functions (Cambridge, 1966).
(11)Srivastava, H. M.On Bessel, Jacobi and Laguerre polynomials. Rend. Sem. Mat. Univ. Padova. 35 (1965), 424432.
(12)Srivastava, H. M.Some expansions in products of hypergeometric functions. Proc. Cambridge Philos. Soc. 62 (1966), 245247.
(13)Srivastava, H. M.The integration of generalized hypergeometric functions. Proc. Cambridge Philos. Soc. 62 (1966), 761764.
(14)Srivastava, H. M.The products of certain classical polynomials. Math. Japon. 11 (1966), 6776.
(15)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).

# Double Meijer transformations of certain hypergeometric functions

## Metrics

### Full text viewsFull text views reflects the number of PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 0 *