An equation of the form , where contains a finite number of independent variables, known functions,
and unknown functions which are to be solved for. Many properties of functions can
be determined by studying the types of functional equations they satisfy. For example,
the gamma function satisfies the functional equations
The following functional equations hold
where
(Borwein et al. 2004).
See also Abel's Duplication Formula ,
Abel's Functional Equation ,
Functional
Analysis ,
Reflection Relation
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References Borwein, J.; Bailey, D.; and Girgensohn, R. Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters,
2004. Castillo, E.; Gutiérrez, J. M.; and Iglesias, A. "Solving
a Functional Equation." Mathematica J. 5 , 82-86, 1995. Castillo,
E. and Iglesias, A. "A Package for Symbolic Solution of Functional Equations."
Mathematics with Vision: Proceedings of the First International Mathematica Symposium.
pp. 85-92, 1995. Flajolet, P. and Sedgewick, R. "Analytic Combinatorics:
Functional Equations, Rational and Algebraic Functions." http://www.inria.fr/RRRT/RR-4103.html . Kuczma,
M. Functional
Equations in a Single Variable. Warsaw, Poland: Polska Akademia Nauk, 1968. Kuczma,
M. An
Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation
and Jensen's Inequality. Warsaw, Poland: Uniwersitet Slaski, 1985. Kuczma,
M.; Choczewski, B.; and Ger, R. Iterative
Functional Equations. Cambridge, England: Cambridge University Press, 1990. Referenced
on Wolfram|Alpha Functional Equation
Cite this as:
Weisstein, Eric W. "Functional Equation."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/FunctionalEquation.html
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