ELLIPTIC; elliptic integrals by duplication. [NAS AS/6; IBM370 (designed to be machine-independent); FORTRAN IV]
ELLIPTIC is a set of four subroutines for numerically evaluating logarithms, arctangents, and elliptic integrals of all three kinds, including complete integrals. Two of the subroutines evaluate the incomplete elliptic integrals of the first and third kinds - RF(x,y,z) =1/2 of the integral with respect to t from 0 to infinity of ((t+x)(t+y)(t+z))**(-1/2), and RJ(x,y,z,p)=3/2 of the integral with respect to t from 0 to infinity of ((t+x)(t+y)(t+z))**(-1/2)/(t+p). The integrals are complete if x=0. The other two subroutines evaluate the special cases RC(x,y)=RF(x,y,y) and RD(x,y,z)=RJ(x,y,z,z). The function RD is an incomplete elliptic integral of the second kind, and RC embraces the logarithm, inverse circular functions, and inverse hyperbolic functions. These functions and others, such as Legendre's elliptic integrals and Heuman's lambda function can be expressed in terms of RC, RF, RD, and RJ (reference 1).NAS AS/6;IBM370 (designed to be machine-independent); FORTRAN IV; OS/MVT (IBM370); NESC used less than 50K bytes on an IBM370/195 for execution of the sample problems..
- Research Organization:
- Ames Lab., IA (USA)
- OSTI ID:
- 6478804
- Report Number(s):
- ANL/NESC-986; ON: DE83048986
- Country of Publication:
- United States
- Language:
- English
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