2010-01-01

# Analytical and Numerical Aspects of a Generalization of the Complementary Error Function

## Publication

### Publication

In this paper we discuss analytical and numerical properties of the function $V_{\nu,\mu}(\alpha,\beta,z)=\int_0^\infty e^{-zt}(t+\alpha)^\nu(t+\beta)^\mu\,dt$, with $\alpha,\beta,\Re z>0$, which can be viewed as a generalization of the complementary error function, and in fact also as a generalization of the Kummer $U-$function. The function $V_{\nu,\mu}(\alpha,\beta,z)$ is used for certain values of the parameters as an approximant in a singular perturbation problem. We consider the relation with other special functions and give asymptotic expansions as well as recurrence relations. Several methods for its numerical evaluation and examples are given.

Additional Metadata | |
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Keywords | complementary error function, singular perturbation problem, incomplete gamma function, confluent hypergeometric function, asymptotic expansions, recurrence relations |

MSC | Computation of special functions, construction of tables (msc 65D20) |

Publisher | Elsevier |

Journal | Applied Mathematics and Computation |

Note | doi:10.1016/j.amc.2010.05.025 |

Citation |
Deaño, A, & Temme, N.M. (2010). Analytical and Numerical Aspects of a Generalization of the Complementary Error Function.
Applied Mathematics and Computation. |