Addition formula for complementary error function with associated integral representations

Authors

  • Leila Moslehi Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran Author
  • Alireza Ansari Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran Author

Keywords:

addition formula, Mellin transform, Laplace transform, complementary error function, Theta function

Subjects:

33B20, 44A10

Abstract

In this paper, using the Mellin transform ofparabolic cylinder functions we present an addition formulafor the complementary error function in terms of the Gaussianfunctions. Also, some inverse Laplace transforms of thecomplementary error functions are shown and new integralrepresentations for the exponential integral and Bessel functionsare given. Moreover, the solution of diffusion equation infinite domain is presented in terms of the theta functions.

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Published

2016-10-15

Issue

Vol. 68 No. 4 (2016): Vol. 68, Issue 4

Section

Articles

License

Copyright (c) 2016 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.