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.

Read more about Reflection Formula: Known Formulae

### Other articles related to "reflection formula, reflection":

**Reflection Formula**- Known Formulae

... 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 ...

**Reflection Formula**

... The digamma function satisfies a

**reflection formula**similar to that of the Gamma function ...

**Reflection Formula**

... The reflection formula can be generalized as follows if we have. ...

### Famous quotes containing the words formula and/or reflection:

“But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the *formula* for that? The *formula* for that is not included in the curriculum.”

—Fannie Hurst (1889–1968)

“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 (1817–1862)