Computation of Jn(x) by numerical integration

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Computation of Jn(x) by numerical integration

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Communications of the ACM archive
Volume 12 , Issue 4 (April 1969) table of contents

Pages: 236 - 238

Year of Publication: 1969

ISSN:0001-0782

Authors

A. H. Stroud	State Univ. of New York at Buffalo
J. P. Kohli	State Univ. of New York at Buffalo

Publisher

ACM New York, NY, USA

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ABSTRACT

It is shown to be practical to compute Jn(x) by numerical integration of its integral representation using the trapezoidal rule. The error in this approximation was studied empirically.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	J. Stafford, Certification of algorithm 21 [S17]: Bessel function for a set of integer orders, Communications of the ACM, v.8 n.4, p.219, April 1965 [doi>10.1145/363831.364867]
	2	FETTIS, H. E. Numerical calculation of certain definite integrals by Poisson's summation formula. Math. Tables Aids Comput. 9 (1955), 85-92.
	3	W. Gautschi, ACM Algorithm 236: Bessel Functions of the First Kind, Communications of the ACM, v.7 n.8, p.479-480, Aug. 1964 [doi>10.1145/355586.355587]
	4	GOLDSTEIN, H., AND THALER, n . M. Recurrence techniques for the calculation of Bessel functions. Math. Tables Aids Comput. 13 (1959), 102-108.
	5	John F. Hart, Computer Approximations, Krieger Publishing Co., Inc., Melbourne, FL, 1978
	6	IBM Corp., System/360 scientific subroutine package (360A- CM-03X) Version II (3rd ed.), 1967, p. 157.
	7	STEGUN, I. A., AND ABRAMOWITZ, M. Generation of Bessel functions on high speed computers. Math. Tables Aids Comput. 11 (1957), 255-257.