Algorithm 895: A continued fractions package for special functions

ABSTRACT

The continued fractions for special functions package (in the sequel abbreviated as CFSF package) complements a systematic study of continued fraction representations for special functions. It provides all the functionality to create continued fractions, in particular k-periodic or limit k-periodic fractions, to compute approximants, make use of continued fraction tails, perform equivalence transformations and contractions, and much more. The package, developed in Maple, includes a library of more than 200 representations of special functions, of which only 10% can be found in the 1964 NBS Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables by M. Abramowitz and I. Stegun.

REFERENCES

• 1: Milton Abramowitz, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,, Dover Publications, Incorporated, 1974
• 2: Annie A.M. Cuyt , Vigdis Petersen , Brigitte Verdonk , Haakon Waadeland , William B. Jones, Handbook of Continued Fractions for Special Functions, Springer Publishing Company, Incorporated, 2008
• 3: Annie Cuyt , Brigitte Verdonk , Haakon Waadeland, Efficient and Reliable Multiprecision Implementation of Elementary and Special Functions, SIAM Journal on Scientific Computing, v.28 n.4, p.1437-1462, 2006 [doi>10.1137/050629203]
• 4: Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. 1953a. Higher Transcendental Functions. Vol. 1. McGraw-Hill, New York.
• 5: Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. 1953b. Higher Transcendental Functions. Vol. 2. McGraw-Hill, New York.
• 6: Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. 1955. Higher Transcendental Functions. Vol. 3. McGraw-Hill, New York.
• 7: L. Jacobsen , H. Waadeland, Convergence acceleration of limit periodic continued fractions under asymptotic side conditions, Numerische Mathematik, v.53 n.3, p.285-298, July 1988 [doi>10.1007/BF01404465]
• 8: Lorentzen, L. and Waadeland, H. 1992. Continued Fractions with Applications. North-Holland, Amsterdam, The Netherlands.
• 9: Lozier, D. 2000. The DMLF project: A new initiative in classical special functions. In Special Functions: Proceedings of the International Workshop, C. Dunkl, M. Ismail, and R. Wong, Eds. World Scientific, Signapore, 9, 207--220.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Special function approximations

General Terms:
Algorithms, Documentation

Keywords:
CAS software, Maple, continued fractions, special functions