Gautschi, Walter The computation of special functions by linear difference equations. (English) Zbl 0892.65008 Elaydi, S. (ed.) et al., Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprém, Hungary, August 7–11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 213-243 (1997). Summary: The use of linear difference equations for the computation of special functions is discussed, especially with regard to numerical stability. The emphasis is on difference equations of the first and second order. Phenomena of instability and pseudostability are exhibited along with numerical algorithms to deal with them.For the entire collection see [Zbl 0885.00051]. Cited in 3 Documents MSC: 65D20 Computation of special functions and constants, construction of tables 65Q05 Numerical methods for functional equations (MSC2000) 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) Keywords:incomplete gamma function; exponential integrals; recurrence algorithm; linear difference equations; numerical stability PDFBibTeX XMLCite \textit{W. Gautschi}, in: Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprém, Hungary, August 7--11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 213--243 (1997; Zbl 0892.65008) Digital Library of Mathematical Functions: §3.6(iii) Miller’s Algorithm ‣ §3.6 Linear Difference Equations ‣ Areas ‣ Chapter 3 Numerical Methods §3.6(vii) Linear Difference Equations of Other Orders ‣ §3.6 Linear Difference Equations ‣ Areas ‣ Chapter 3 Numerical Methods