A code to evaluate modified bessel functions based on thecontinued fraction method

✍ Scribed by J. Segura; P. Fernández de Córdoba; Yu.L. Ratis

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 446 KB
• Volume: 105
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/s0010-4655(97)00069-6

✦ Synopsis

We present an algorithm to evaluate the modified Bessel functions Iv and K,, of integral and half-integral order based on the calculation of the continued fraction for the l',s, the Wronskian and the application of forward recurrence relations for the K~s and backward recurrence for the l'~s. The main feature of the algorithm is that it does not require recalculations using normalization relations nor trial values to start the recurrences; the code evaluates in each step (already normalized) Bessei functions. The accuracy of the method ( 10 -16 for half-integral order and better than 2 x 10 -7 for integral order in our code) is limited only by the precision in the initial values for the recurrence and the maximum order available for a given value of the argument is restricted only by the maximum real number available in the computer.