@article{CM_1962-1964__15__239_0, author = {Braaksma, B. L. J.}, title = {Asymptotic expansions and analytic continuations for a class of {Barnes-integrals}}, journal = {Compositio Mathematica}, pages = {239--341}, publisher = {Kraus Reprint}, volume = {15}, year = {1962-1964}, mrnumber = {167651}, zbl = {0129.28604}, language = {en}, url = {http://www.numdam.org/item/CM_1962-1964__15__239_0/} }
TY - JOUR AU - Braaksma, B. L. J. TI - Asymptotic expansions and analytic continuations for a class of Barnes-integrals JO - Compositio Mathematica PY - 1962-1964 SP - 239 EP - 341 VL - 15 PB - Kraus Reprint UR - http://www.numdam.org/item/CM_1962-1964__15__239_0/ LA - en ID - CM_1962-1964__15__239_0 ER -
Braaksma, B. L. J. Asymptotic expansions and analytic continuations for a class of Barnes-integrals. Compositio Mathematica, Tome 15 (1962-1964), pp. 239-341. http://www.numdam.org/item/CM_1962-1964__15__239_0/
Complex Analysis. New York, 1953. | Zbl
[1]The asymptotic expansion of integral functions defined by Taylor's series. Phil. Trans. Roy. Soc. London (A), 206, 249-297 (1906). | JFM
[2][3] The asymptotic expansion of integral functions defined by generalized hypergeometric series. Proc. London Math. Soc. (2), 5, 59-116 (1907). | JFM
[4] A new development of the theory of the hypergeometric functions. Proc. London Math. Soc. (2), 6, 141-177 (1908). | JFM
Some properties of modular relations. Ann. of Math. 53, 332-363 (1951). | Zbl
[5][5a] Theorems on analytic continuation which occur in the study of Riemann's functional equation. Journ. Indian Math. Soc., New Series 21, 127-147 (1957). | Zbl
[6] On Riemann's functional equation with multiple gamma factors. Ann. of Math. 67, 29-41 (1958). | Zbl
On a function, which is a special case of Meijer's G-function. Compos. Math. 15, 34-63 (1962). | Numdam | Zbl
[7]An introduction to the theory of infinite series. 2nd ed., London, 1949. | JFM | Zbl
[8]Functional equations with multiple gamma factors and the average order of arithmetical functions. Ann. of Math. 76, 93-136 (1962). | Zbl
and [9]An introduction to the theory of functions of a complex variable. Oxford, 1950. | Zbl
[10]On the coefficients in certain asymptotic factorial expansions I, II. Proc. Kon. Ned. Akad. Wet. Ser. A, 60, 337-351 (1957). | Zbl
[11]A class of discontinuous integrals. Quart. Journ. Math. Oxford Ser. 7, 81-96 (1936). | JFM | Zbl
and [12]Handbuch der Laplace-Transformation I, II Basel, 1950, 1955. | Zbl
[13]Asymptotic expansions. New York, 1956. | MR | Zbl
[14]Higher transcendental functions I. New York, 1953. | Zbl
, , , [15]The asymptotic developments of functions defined by Maclaurin series. Ann Arbor, 1936. | JFM | Zbl
[16]The asymptotic expansion of generalized hypergeometric functions. Proc. London Math. Soc. (2), 27, 389-400 (1928). | JFM
[17][18] The G and H functions as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 98, 395-429 (1961). | Zbl
On the asymptotic expansions of entire functions defined by Maclaurin series. Bull. Amer. Math. Soc. 50, 425-430 (1944). | MR | Zbl
[19][20] The asymptotic developments of a class of entire functions. Bull. Amer. Math. Soc. 51, 456-461 (1945). | Zbl
Induction proofs of the relations between certain asymptotic expansions and corresponding generalized hypergeometric series. Proc. Roy. Soc. Edinburgh 58, 1-13 (1938). | JFM | Zbl
[21 ]On the G-function I-VIII. Proc. Kon. Ned. Akad. Wet. 49, 227-237, 344-356, 457-469, 632-641, 765-772, 936-943, 1063-1072, 1165-1175 (1946). | Zbl
[22]On the character of certain entire functions in distant portions of the plane. Amer. J. Math. 60, 561-572 (1938). | JFM | Zbl
[23][24] The asymptotic behavior of a class of entire functions. Amer. J. Math. 65, 450-454 (1943). | Zbl
Note on the asymptotic expansion of generalized hypergeometric functions. Journ. London Math. Soc. 28, 462-464 (1953). | MR | Zbl
[25]On the coefficients in asymptotic factorial expansions. Proc. Amer. Math. Soc. 7, 245-249 (1956). | MR | Zbl
[26]A proof of the asymptotic series for log Γ(z) and log Γ(z+a). Ann. of Math. Second Ser. 32, 10-16 (1931). | JFM | Zbl
[27]Lectures on the theory of functions of a complex variable I. Groningen, 1960. | Zbl
and [28]A class of integral functions defined by Taylor's series. Trans. Cambr. Phil. Soc. 22, 15-37 (1913). | JFM
[29]A course of modern analysis. 4th ed. Cambridge, 1958. | JFM
and [30]The asymptotic expansion of the generalized Bessel function. Proc. London Math. Soc. (2), 38, 257-270 (1935). | JFM | Zbl
[31][32] The asymptotic expansion of the generalized hypergeometric function. Journ. London Math. Soc. 10, 286-293 (1935). | JFM | Zbl
[33] The asymptotic expansion of integral functions defined by Taylor series. Phil. Trans. Roy. Soc. London (A) 238, 423-451 (1940). | JFM | MR | Zbl
[34] The asymptotic expansion of the generalized hypergeometric function. Proc. London Math. Soc. (2) 46, 389-408 (1940). | JFM | MR | Zbl
[35] The generalized Bessel function of order greater than one. Quart. Journ. Math. Oxford Ser. 11, 36-48 (1940). | JFM | MR | Zbl
[36] The asymptotic expansion of integral functions defined by Taylor series (second paper). Phil. Trans. Roy. Soc. London (A) 239, 217-222 (1946). | Zbl
[37] A recursion formula for the coefficients in an asymptotic expansion. Proc. Glasgow Math. Ass. 4, 38-41 (1959-1960). | Zbl
An asymptotic formula for the hypergeometric function 0Δ4 (z). Philos. Magazine (6) 41, 161-173 (1921). | JFM
[38][39] A generalized hypergeometric function with n parameters. Philos. Magazine (6) 41, 174-186 (1921).
[40] Some approximations to hypergeometric functions. Philos. Magazine (6) 45, 818-827 (1923). | JFM