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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.It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.
Reflection and transmittance for two dielectrics [permanent dead link ] – Mathematica interactive webpage that shows the relations between index of refraction and reflection. A self-contained first-principles derivation of the transmission and reflection probabilities from a multilayer with complex indices of refraction.
A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
In mathematics, the Riemann xi function is a variant of the Riemann zeta function, ... The functional equation (or reflection formula) for Landau's ...
The difference equation for the G-function, in conjunction with the functional equation for the gamma function, can be used to obtain the following reflection formula for the Barnes G-function (originally proved by Hermann Kinkelin):
In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, [1] is a technique that provides an analytic expression for the Mellin transform of an analytic function. Page from Ramanujan's notebook stating his Master theorem.
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: [1] [2] [3] ... which both spring off the reflection formula via
The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...