Asymptotic computation of the repeated integrals of the error function complement

Author:
W. R. Wilcox

Journal:
Math. Comp. **18** (1964), 98-105

MSC:
Primary 65.25

DOI:
https://doi.org/10.1090/S0025-5718-1964-0158101-8

MathSciNet review:
0158101

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Abstract | References | Similar Articles | Additional Information

Abstract: Previously, the complementary error function and its repeated integrals were given only for small values of the argument. Several new calculation techniques are derived which permit evaluation for the complete range of the argument. Some new values of these functions for large values of the argument are calculated. These values are plotted in such a manner that approximate values can easily be found for all values of *x*.

**[1]**D. R. Hartree, ``Some properties and applications of the repeated integrals of the error function,''*Mem. Manchester Lit. and Phil. Soc.*, v. 80, 1935, p. 85-102.**[2]**H. S. Carslaw and J. C. Jaeger,*Conduction of Heat in Solids*, Oxford, at the Clarendon Press, 1947. MR**0022294****[3]**Joseph Kaye & V. C. M. Yeh, ``Design charts for transient temperature distribution resulting from aerodynamic heating at supersonic speeds,''*J. Aeronautical Sciences*, v. 22, 1955, p. 755-763.**[4]**Joseph Kaye,*A table of the first eleven repeated integrals of the error function*, J. Math. and Phys.**34**(1955), 119–125. MR**0069575**, https://doi.org/10.1002/sapm1955341119**[5]**British Association For Advancement Of Science,*Mathematical Tables*, University Press, Cambridge, 1951, v. I, Table XV.**[6]**J. Arthur Greenwood and H. O. Hartley,*Guide to tables in mathematical statistics*, Princeton University Press, Princeton, N.J., 1962. MR**0154350****[7]**A. Fletcher, J. C. P. Miller, L. Rosenhead, and L. J. Comrie,*An index of mathematical tables. Vol. I: Introduction. Part I: Index according to functions*, Second edition, Published for Scientific Computing Service Ltd., London, by Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962. MR**0142796**

A. Fletcher, J. C. P. Miller, L. Rosenhead, and L. J. Comrie,*An index of mathematical tables. Vol. II. Part II: Bibliography. Part III: Errors. Part IV: Index to Introduction and Part I*, Second edition, Published for Scientific Computing Service Ltd., London, by Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962. MR**0142797****[8]**O. S. Beryland, R. I. Gavrilova & A. P. Prudnikov,*Tables of Integral Error Functions and Hermite Polynomials*, Pergamon Press, Oxford, 1962.**[9]**Nat. Bur. Standards,*Tables of the Error Function and Its Derivative*, Applied Math. Series No. 41, 1954.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1964-0158101-8

Article copyright:
© Copyright 1964
American Mathematical Society