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

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**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 ...

**Reflection Formula**

... The digamma function satisfies a

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**Reflection Formula**

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

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“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 child’s 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.”

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“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)