Numerical integration of bessel functions of high order

Lucien De Corte; R. De Meersman

Numerical integration of bessel functions of high order

Lucien De Corte, R. De Meersman

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Abstract

The integral 1/2 _a∫^b J_n² (x) [1-2x k_m-1(x) l_m (x)] dx defined for large positive values of n, m and B (A ≥ 0) has been calculated by an autocode program, written for the Ferranti-Mercury computer. A convergent continued fraction was used to calculate the Bessel functions J_n (x) and the modified ones I_m (x). The modified function K_m-1 (x) was obtained from its recurrence relation.

Original language	English
Publisher	SCK CEN
Number of pages	8
State	Published - Jan 1967

Publication series

Name	SCK CEN Reports
Publisher	SCK CEN
No.	BLG-420

Access to Document

BLG-420Final published version, 3.05 MBLicense: Unspecified

Cite this

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title = "Numerical integration of bessel functions of high order",

abstract = "The integral 1/2 a∫b Jn2 (x) [1-2x km-1(x) lm (x)] dx defined for large positive values of n, m and B (A ≥ 0) has been calculated by an autocode program, written for the Ferranti-Mercury computer. A convergent continued fraction was used to calculate the Bessel functions Jn (x) and the modified ones Im (x). The modified function Km-1 (x) was obtained from its recurrence relation. ",

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N2 - The integral 1/2 a∫b Jn2 (x) [1-2x km-1(x) lm (x)] dx defined for large positive values of n, m and B (A ≥ 0) has been calculated by an autocode program, written for the Ferranti-Mercury computer. A convergent continued fraction was used to calculate the Bessel functions Jn (x) and the modified ones Im (x). The modified function Km-1 (x) was obtained from its recurrence relation.

AB - The integral 1/2 a∫b Jn2 (x) [1-2x km-1(x) lm (x)] dx defined for large positive values of n, m and B (A ≥ 0) has been calculated by an autocode program, written for the Ferranti-Mercury computer. A convergent continued fraction was used to calculate the Bessel functions Jn (x) and the modified ones Im (x). The modified function Km-1 (x) was obtained from its recurrence relation.

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