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
Famous quotes containing the words reflection and/or formula:
“Water. Its sunny track in the plain; its splashing in the garden canal, the sound it makes when in its course it meets the mane of the grass; the diluted reflection of the sky together with the fleeting sight of the reeds; the Negresses fill their dripping gourds and their red clay containers; the song of the washerwomen; the gorged fields the tall crops ripening.”
—Jacques Roumain (19071945)
“Hidden away amongst Aschenbachs writing was a passage directly asserting that nearly all the great things that exist owe their existence to a defiant despite: it is despite grief and anguish, despite poverty, loneliness, bodily weakness, vice and passion and a thousand inhibitions, that they have come into being at all. But this was more than an observation, it was an experience, it was positively the formula of his life and his fame, the key to his work.”
—Thomas Mann (18751955)