The evaluation of Bessel functions via exp-arc integrals

Journal of Mathematical Analysis and Applications

Volumn 341, Issue 1, 2008, Pages 478-500

  Borwein, David ^a   Borwein, Jonathan M ^b   Chan, O Yeat ^b  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b DALHOUSIE UNIVERSITY   (Canada)

Author keywords

Bessel function; Exponential hyperbolic expansions; Uniform series expansion

Indexed keywords

EID: 38749137011     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.10.003     Document Type: Article

References (15)

1. Borwein D., Borwein J.M., and Crandall R. Effective Laguerre asymptotics. preprint at. http://locutus.cs.dal.ca:8088/archive/00000334/
2. Borwein J.M., and Chan O.-Y. Uniform bounds for the complementary incomplete gamma function. preprint at. http://locutus.cs.dal.ca:8088/archive/00000335/
3. The NIST Digital Library of Mathematical Functions, at http://dlmf.nist.gov
4. Paris R.B. On the use of Hadamard expansions in hyperasymptotic evaluation, I. Real variables. Proc. R. Soc. Lond. Ser. A 457 (2001) 2835-2853
5. Paris R.B. On the use of Hadamard expansions in hyperasymptotic evaluation, II. Complex variables. Proc. R. Soc. Lond. Ser. A 457 (2001) 2855-2869
6. Paris R.B. On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals, I. Real variable. J. Comput. Appl. Math. 167 (2004) 293-319
7. Paris R.B. On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals, II. Complex variable. J. Comput. Appl. Math. 167 (2004) 321-343
8. R.B. Paris, On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals, III. Clusters of saddle points, J. Comput. Appl. Math., in press
9. R.B. Paris, On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals, IV. Poles, J. Comput. Appl. Math., in press
10. Paris R.B. Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. R. Soc. Lond. Ser. A 460 (2004) 2737-2759
11. Paris R.B., and Kaminski D. Hadamard expansions for integrals with saddles coalescing with an endpoint. Appl. Math. Lett. 18 (2005) 1389-1395
12. R.B. Paris, private communication via R. Crandall, 2007
13. Stromberg K.R. Classical Real Analysis (1981), Wadsworth, Belmont, CA
14. Watson G.N. A Treatise on the Theory of Bessel Functions. second ed. (1980), Cambridge Univ. Press
15. Zhang S., and Jin J. Computation of Special Functions (1996), John Wiley & Sons