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Zbl 0892.65008
Gautschi, Walter
The computation of special functions by linear difference equations. (English)
[A] 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). ISBN 90-5699-521-9/hbk

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.

MSC 2000:: *65D20 Computation of special functions
65Q05 Numerical methods for functional equations
33B20 Incomplete beta and gamma functions

Keywords: incomplete gamma function; exponential integrals; recurrence algorithm; linear difference equations; numerical stability

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