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 ... functions, and for 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 defined as the derivations of the and thus its ...
... 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. ...
Famous quotes containing the words formula and/or reflection:
“In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the childs age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.”
—Alicia F. Lieberman (20th century)
“But before the extremity of the Cape had completely sunk, it appeared like a filmy sliver of land lying flat on the ocean, and later still a mere reflection of a sand-bar on the haze above. Its name suggests a homely truth, but it would be more poetic if it described the impression which it makes on the beholder.”
—Henry David Thoreau (18171862)