# Accession Number:

## ADA034434

# Title:

## Factorial and Hadamard Series for Bessel Functions of Orders Zero and One.

# Descriptive Note:

## Memorandum rept.,

# Corporate Author:

## BALLISTIC RESEARCH LABS ABERDEEN PROVING GROUND MD

# Personal Author(s):

# Report Date:

## 1976-12-01

# Pagination or Media Count:

## 20.0

# Abstract:

Bessel functions of orders zero and one for moderate and large positve arguments have been programmed in FORTRAN using factorial series for J sub nx, Y sub nx and K sub nx and Hadamard series for I sub n x. A subroutine to calculate Stirling numbers of the first kind was developed for use in the factorial series. The recurrence relation was modified and the resulting Stirling numbers scaled so that the entire range of the computer was utilized e.g., 10 to the minus 150th power s 10 to the 150th power instead of s 10 to the 150th power. In this way, more terms of the series can be calculated and higher accuracy obtained. For use in the Hadamard series, a subroutine to calculate incomplete gamma functions was developed. Various algorithms were necessary to encompass the required range of arguments. These programs were devised to verify the accuracy for moderate and large arguments of our previously developed Bessel function subroutine. These programs replace the asymptotic series with convergent series, which, of course, is desirable. Extension of the program to complex arguments is now in progress.

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Computer Programming and Software