Generation of Spherical Bessel Functions in Digital Computers

ABSTRACT

A method of computation for spherical Bessel functions of real and imaginary argument is given which is especially suitable for high speed digital computers. The accuracy and convergence are examined and criterion formulas are given. A procedure based on the Wronskian is used to simplify the final normalization.

REFERENCES

• 1: As M. Abramowitz has kindly pointed out to us, the earliest known application of the ratio method of recursion with unnormalized functions rather than with the functions themselves is found in: j. C. P. MILLER, British Association for the Advancement of Science, Mathematical Tables, Vol. X, Bessel Function8, Part II, University Press (Cambridge) 1952, p. xvi.
• 2: The ratio method was used for desk calculation by C. W. JONES, A Short Table for the Bessel Functions Univcxsity Press, Cambridge (1952).
• 3: The ratio method for the generation of the cylindrical functions J(x) and Y,(x) is described by: J. B. RANDELS AND R. F. REEVES, Cornmunications A CM, l (May 1958).
• 4: P. M. MORSE. AND H.FESHBACH, Methods of Theoretical Physics, MeGraw-HiU (New York) 1953, p. 1573.
• 5: M. SAFFREN, Physics Department, Massachusetts Institute of Technology, Cambridge, Mass. (private communication).
• 6: In the case of the i,(x) a weaker expression for is given by: F. J. CORBATO, J. Chem. Phys. 24, 452 (1956).

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.3 Studies of Program Constructs
          Subjects: Functional constructs

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Measurement, Performance, Theory