Further approximations for elliptic integrals
Abstract: The present paper develops approximations for the three kinds of elliptic integrals based on the Padé approximations for the square root. The work includes and extends our previous work on the subject to provide efficient approximations over a larger part of the complex and planes.
-  Yudell L. Luke, Approximations for elliptic integrals, Math. Comp. 22 (1968), 627–634. MR 0226825, https://doi.org/10.1090/S0025-5718-1968-0226825-3
-  Yudell L. Luke, The Special Functions and Their Approximations, Vol. 2, Academic Press, New York, 1969, pp. 269-273.
-  H. Van de Vel, On the series expansion method for computing incomplete elliptic integrals of the first and second kinds, Math. Comp. 23 (1969), 61–69. MR 0239732, https://doi.org/10.1090/S0025-5718-1969-0239732-8
- Yudell L. Luke, "Approximations for elliptic integrals," Math. Comp., v. 22, 1968, pp. 627-634. MR 37 #2412. MR 0226825 (37:2412)
- Yudell L. Luke, The Special Functions and Their Approximations, Vol. 2, Academic Press, New York, 1969, pp. 269-273.
- H. van de Vel, "On the series expansion method for computing elliptic integrals of the first and second kinds," Math Comp., v. 23, 1969, pp. 61-70. MR 0239732 (39:1089)
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Keywords: Elliptic integrals, approximations by rational functions
Article copyright: © Copyright 1970 American Mathematical Society