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  2. Reflection formula - Wikipedia

    en.wikipedia.org/wiki/Reflection_formula

    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.

  3. Fresnel equations - Wikipedia

    en.wikipedia.org/wiki/Fresnel_equations

    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.

  4. Reflection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Reflection_(mathematics)

    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.

  5. Riemann xi function - Wikipedia

    en.wikipedia.org/wiki/Riemann_Xi_function

    In mathematics, the Riemann xi function is a variant of the Riemann zeta function, ... The functional equation (or reflection formula) for Landau's ...

  6. Barnes G-function - Wikipedia

    en.wikipedia.org/wiki/Barnes_G-function

    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):

  7. Ramanujan's master theorem - Wikipedia

    en.wikipedia.org/wiki/Ramanujan's_master_theorem

    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.

  8. Digamma function - Wikipedia

    en.wikipedia.org/wiki/Digamma_function

    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

  9. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    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 ...