Abstract
A great many of the special functions of mathematical physics which arise in particular problems can be expressed as a chain of homogeneous fractional-Laplace operators. A convenient way of cataloging these formulas is given by the G-function of Meijer. We define these operators and apply them to a few simple examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Meller, N. A., “On Certain Applications of the Operational Calculus to Problems of Analysis,” Zh. vych. mat., 3, No 1(1963) pp 71–78
Kober, H, “On Fractional Integrals and Derivatives,” Quart. J. Math. (1) (1940), pp. 193–311
Erdélyi, A and H. Kober, “Some Remarks on Hankel Transforms,” Quart. J. Math (1) (1940) pp. 212–221
Erdélyi, A et al, Higher Transcendental Functions, vol 1 and 2, McGraw-Hill (1953)
Luke, Y., The Special Functions and Their Approximations, vol. 1 and 2, Academic Press (1969)
Editor information
Rights and permissions
Copyright information
© 1975 Springer-Verlag
About this chapter
Cite this chapter
Higgins, T.P. (1975). A child's garden of special functions. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067106
Download citation
DOI: https://doi.org/10.1007/BFb0067106
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07161-7
Online ISBN: 978-3-540-69975-0
eBook Packages: Springer Book Archive