A special function is a function (usually named after an early investigator of its properties) having a particular use in mathematical physics or some other branch of mathematics. Prominent examples include the gamma function, hypergeometric function, Whittaker function, and Meijer G-function.
Special Function
See also
Elementary Function, First Kind, Function, Second Kind, Third KindExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.Andrews, G. E.; Askey, R.; and Roy, R. Special Functions. Cambridge, England: Cambridge University Press, 1999.Arscott, F. M. "The Land Beyond Bessel: A Survey of Higher Special Functions." In Ordinary and Partial Differential Equations (Ed. W. N. Everitt and B. D. Sleeman). New York: Springer-Verlag, pp. 26-45, 1981.Luke, Y. L. The Special Functions and their Approximations, Vol. 1. New York: Academic Press, 1969.Luke, Y. L. The Special Functions and their Approximations, Vol. 2. New York: Academic Press, 1969.Magnus, W. and Oberhettinger, F. Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed. New York: Springer-Verlag, 1966.Nikiforov, A. F. and Uvarov, V. B. Special Functions of Mathematical Physics: A Unified Introduction with Applications. Boston, MA: Birkhäuser, 1988.National Institute of Standards. "Digital Library of Mathematical Functions." http://dlmf.nist.gov/.Prudnikov, A. P.; Brychkov, Yu. A.; and Marichev, O. I. Integrals and Series, Vol. 1: Elementary Functions. New York: Gordon and Breach, 1986.Prudnikov, A. P.; Brychkov, Yu. A.; and Marichev, O. I. Integrals and Series, Vol. 2: Special Functions. New York: Gordon and Breach, 1990.Prudnikov, A. P.; Brychkov, Yu. A.; and Marichev, O. I. Integrals and Series, Vol. 3: More Special Functions. New York: Gordon and Breach, 1989.Prudnikov, A. P.; Brychkov, Yu. A.; and Marichev, O. I. Integrals and Series, Vol. 4: Direct Laplace Transforms. New York: Gordon and Breach, 1992.Prudnikov, A. P.; Brychkov, Yu. A.; and Marichev, O. I. Integrals and Series, Vol. 5: Inverse Laplace Transforms. New York: Gordon and Breach, 1992.Spanier, J.; Myland, J.; and Oldham, K. B. An Atlas of Functions, 2nd ed. Washington, DC: Hemisphere, 1987.Weisstein, E. W. "Books about Special Functions." http://www.ericweisstein.com/encyclopedias/books/SpecialFunctions.html.Wolfram Research, Inc. "Wolfram Research's Mathematical Functions." http://functions.wolfram.com.Referenced on Wolfram|Alpha
Special FunctionCite this as:
Weisstein, Eric W. "Special Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpecialFunction.html