Work

An Integral Representation for the Modified Bessel Function of the Third Kind, Computable for Large, Imaginary Order

Year: 1967

Type: article

Abstract: ¿erfc2and z2 erfc z correct to 6 significant figures (7 s.f. for z > 1) using single precision on a computer with word length of 8 decimal places, for all z for which e~z* can be calculated correctly.To obtain greater accuracy, it is necessary either to use double precision or to use more than two different expansions for each function.From Gautschi's formula [2] for the number of terms required for calculation by backward recurrence, we see that that method will be better (for 7 s.f.accuracy) if all the z's of interest are greater than about 2.5.The advantage accruing from the use of Chebyshev approximations would be still greater for multiple-precision calculations of very high accuracy.

Source: Mathematics of Computation

DOI: 10.1090/s0025-5718-67-99143-0

Authors: James D. Lear, James E. Sturm

Institution: Battelle

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Lehigh University, York University, Centers for Disease Control and Prevention, Division of Mathematical Sciences

OpenAlex ID: W1983392478