Evaluation of the integral
Authors:
K. S. Nagaraja and G. R. Verma
Journal:
Math. Comp. 39 (1982), 179194
MSC:
Primary 65D20; Secondary 65A05, 65D30
MathSciNet review:
658222
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Abstract: The representations of the above integral, in a power series form for small values of x and in an asymptotic form for large values of x, are given for integer values of n. In view of the usefulness of this integral, tabulated values are also presented for a wide range of values of x and p, and for a few values of n.
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 M. Abramowitz, "Evaluation of the integral ," J. Math. Phys., v. 32, 1953, pp. 188192. MR 0057391 (15:219c)
 [2]
 A. Erdélyi, "Note on the paper 'On a definite integral' by R. H. Ritchie," MTAC, v. 4, 1950, p. 179.
 [3]
 E. T. Goodwin & J. Staton, "Tables of ," Quart J. Mech. Appl. Math., v. 1, 1948, pp. 319322. MR 0027177 (10:268a)
 [4]
 Y. L. Luke, Integrals of Bessel Functions, McGrawHill, New York, 1962, p. 186. MR 0141801 (25:5198)
 [5]
 K. S. Nagaraja, "Concerning the value of ," J. Math. and Phys., v. 44, 1965, pp. 182188. MR 0178163 (31:2421)
 [6]
 F. W. J. Olver, Asymptotic Expansions and Special Functions, Academic Press, New York, 1975. MR 0393977 (52:14784)
 [7]
 R. H. Ritchie "On a definite integral," MTAC, v. 4, 1950, pp. 7577. MR 0043273 (13:234a)
 [8]
 N. M. Temme, "Uniform asymptotic expansions of confluent hypergeometric functions," J. Inst. Math. Appl., v. 22, 1978, pp. 215223. MR 509160 (80a:33004)
 [9]
 N. M. Temme, "The asymptotic expansions of the incomplete gamma functions," SIAM J. Math. Anal., v. 10, 1979, pp. 757766. MR 533947 (80i:33002)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206582228
PII:
S 00255718(1982)06582228
Article copyright:
© Copyright 1982 American Mathematical Society
