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
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
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.
 [1]
Milton
Abramowitz, Evaluation of the integral
∫^{∞}₀𝑒^{𝑢²𝑥/𝑢}𝑑𝑢.,
J. Math. Physics 32 (1953), 188–192. 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 and J.
Staton, Table of
∫^{∞}₀(𝑒^{𝑢²}/𝑢+𝑥)𝑑𝑢,
Quart. J. Mech. Appl. Math. 1 (1948), 319–326. MR 0027177
(10,268a)
 [4]
Yudell
L. Luke, Integrals of Bessel functions, McGrawHill Book Co.,
Inc., New YorkTorontoLondon, 1962. MR 0141801
(25 #5198)
 [5]
K.
S. Nagaraja, Concerning the value of
∫^{𝑝}₀𝑒^{𝑢²}\over𝑢+𝑥𝑑𝑢,
J. Math. and Phys. 44 (1965), 182–188. MR 0178163
(31 #2421)
 [6]
F.
W. J. Olver, Unsolved problems in the asymptotic estimation of
special functions, Theory and application of special functions (Proc.
Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975)
Academic Press, New York, 1975, pp. 99–142. Math. Res. Center,
Univ. Wisconsin, Publ. No. 35. MR 0393977
(52 #14784)
 [7]
R.
H. Ritchie, On a definite integral, Math. Tables and Other Aids to Computation 4 (1950), 75–77. MR 0043273
(13,234a), http://dx.doi.org/10.1090/S00255718195000432736
 [8]
N.
M. Temme, Uniform asymptotic expansions of confluent hypergeometric
functions, J. Inst. Math. Appl. 22 (1978),
no. 2, 215–223. MR 509160
(80a:33004)
 [9]
N.
M. Temme, The asymptotic expansion of the incomplete gamma
functions, SIAM J. Math. Anal. 10 (1979), no. 4,
757–766. MR
533947 (80i:33002), http://dx.doi.org/10.1137/0510071
 [1]
 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)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65D20,
65A05,
65D30
Retrieve articles in all journals
with MSC:
65D20,
65A05,
65D30
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206582228
PII:
S 00255718(1982)06582228
Article copyright:
© Copyright 1982
American Mathematical Society
