Reduction and evaluation of elliptic integrals
نویسندگان
چکیده
منابع مشابه
Three Improvements in Reduction and Computation of Elliptic Integrals
Three improvements in reduction and computation of elliptic integrals are made. 1. Reduction formulas, used to express many elliptic integrals in terms of a few standard integrals, are simplified by modifying the definition of intermediate "basic integrals." 2. A faster than quadratically convergent series is given for numerical computation of the complete symmetric elliptic integral of the thi...
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In [16], the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) a...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1966
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1966-0215497-8