A table of elliptic integrals: two quadratic factors
Author:
B. C. Carlson
Journal:
Math. Comp. 59 (1992), 165180
MSC:
Primary 65D20; Secondary 33C75, 33E05
MathSciNet review:
1134720
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Thirteen integrands that are rational except for the square root of a quartic polynomial with two pairs of conjugate complex zeros are integrated in terms of Rfunctions of real variables. In contrast with previous tables, the formulas hold for all real intervals of integration for which the integrals exist (possibly as Cauchy principal values). This is achieved by using Landen's transformation and the duplication theorem. In an appendix, an elliptic integral of the third kind with a restricted complex parameter is transformed to make the parameter real. Also, a degenerate integral of the first kind is separated into real and imaginary parts.
 [1]
Paul
F. Byrd and Morris
D. Friedman, Handbook of elliptic integrals for engineers and
scientists, Die Grundlehren der mathematischen Wissenschaften, Band
67, SpringerVerlag, New YorkHeidelberg, 1971. Second edition, revised. MR 0277773
(43 #3506)
 [2]
Billie
Chandler Carlson, Special functions of applied mathematics,
Academic Press [Harcourt Brace Jovanovich, Publishers], New YorkLondon,
1977. MR
0590943 (58 #28707)
 [3]
B.
C. Carlson, Elliptic integrals of the first kind, SIAM J.
Math. Anal. 8 (1977), no. 2, 231–242. MR 0430341
(55 #3346)
 [4]
B.
C. Carlson, A table of elliptic integrals of the
second kind, Math. Comp.
49 (1987), no. 180, 595–606, S13–S17. MR 906192
(89b:65013), http://dx.doi.org/10.1090/S00255718198709061921
 [5]
B.
C. Carlson, A table of elliptic integrals of the
third kind, Math. Comp. 51
(1988), no. 183, 267–280,
S1–S5. MR
942154 (89k:33003), http://dx.doi.org/10.1090/S00255718198809421547
 [6]
B.
C. Carlson, A table of elliptic integrals: cubic
cases, Math. Comp. 53
(1989), no. 187, 327–333. MR 969482
(89m:65009), http://dx.doi.org/10.1090/S00255718198909694824
 [7]
B.
C. Carlson, Landen transformations of integrals, Asymptotic
and computational analysis (Winnipeg, MB, 1989) Lecture Notes in Pure and
Appl. Math., vol. 124, Dekker, New York, 1990, pp. 75–94.
MR
1052430 (91m:33026)
 [8]
B.
C. Carlson, A table of elliptic integrals: one
quadratic factor, Math. Comp.
56 (1991), no. 193, 267–280. MR 1052087
(92b:33056), http://dx.doi.org/10.1090/S00255718199110520876
 [9]
I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York, 1980.
 [1]
 P. F. Byrd and M. D. Friedman, Handbook of elliptic integrals for engineers and scientists, 2nd ed., SpringerVerlag, New York, 1971. MR 0277773 (43:3506)
 [2]
 B. C. Carlson, Special functions of applied mathematics, Academic Press, New York, 1977. MR 0590943 (58:28707)
 [3]
 , Elliptic integrals of the first kind, SIAM J. Math. Anal. 8 (1977), 231242. MR 0430341 (55:3346)
 [4]
 , A table of elliptic integrals of the second kind, Math. Comp. 49 (1987), 595606. (Supplement, ibid., S13S17.) MR 906192 (89b:65013)
 [5]
 , A table of elliptic integrals of the third kind, Math. Comp. 51 (1988), 267280. (Supplement, ibid., S1S5.) MR 942154 (89k:33003)
 [6]
 , A table of elliptic integrals: cubic cases, Math. Comp. 53 (1989), 327333. MR 969482 (89m:65009)
 [7]
 , Landen transformations of integrals, Asymptotic and Computational Analysis (R. Wong, ed.), Marcel Dekker, New York, 1990, pp. 7594. MR 1052430 (91m:33026)
 [8]
 , A table of elliptic integrals: one quadratic factor, Math. Comp. 56 (1991), 267280. MR 1052087 (92b:33056)
 [9]
 I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York, 1980.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65D20,
33C75,
33E05
Retrieve articles in all journals
with MSC:
65D20,
33C75,
33E05
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199211347204
PII:
S 00255718(1992)11347204
Article copyright:
© Copyright 1992
American Mathematical Society
