In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation, and it is very common in the literature to use the term "functional equation" when "reflection formula" is meant.
Reflection formulas are useful for numerical computation of special functions. In effect, an approximation that has greater accuracy or only converges on one side of a reflection point (typically in the positive half of the complex plane) can be employed for all arguments.
Other articles related to "reflection formula, reflection":
... The even and odd functions satisfy simple reflection relations around a = 0 ... all odd functions, A famous relationship is Euler's reflection formula for the Gamma function Γ(z), due to Leonhard Euler ... There is also a reflection formula for the general n-th order polygamma function ψ(n)(z), which springs trivally from the fact that the polygamma functions are ...
... The digamma function satisfies a reflection formula similar to that of the Gamma function ...
... The reflection formula can be generalized as follows if we have. ...
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