complex analysis, the Schwarz triangle function or Schwarz s-function is a function that conformally maps the upper half plane to a triangle in the upper half...

In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere (spherical tiling), possibly overlapping...

theorem Schwarz reflection principle Schwarz triangle Schwarz triangle function Cauchy–Schwarz inequality Theorem of Pohlke and Schwarz Schwarz, H. A....

differential equation and f(z) is the Schwarz triangle function, which can be written in terms of hypergeometric functions. For a quadrilateral the accessory...

hypergeometric functions or incomplete beta functions. The upper half-plane is mapped to a triangle with circular arcs for edges by the Schwarz triangle map. The...

The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner...

In geometry, an isosceles triangle (/aɪˈsɒsəliːz/) is a triangle that has two sides of equal length and two angles of equal measure. Sometimes it is specified...

diverge. The Schwarz lantern demonstrates that sampling a curved surface by close-together points and connecting them by small triangles is inadequate...

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length...

Schwarzian derivative (Hille 1976, pp. 307–401). The Schwarz triangle maps or Schwarz s-functions are ratios of pairs of solutions. s k ( z ) = ϕ k ( 1...

of triangle groups, of which 12 are Hurwitz groups (quotients of the (2,3,7) group). Schwarz triangle The Schwarz triangle map is a map of triangles to...

special functions, Schwarz's list or the Schwarz table is the list of 15 cases found by Hermann Schwarz (1873, p. 323) when hypergeometric functions can be...

exceptional Schwarz triangles (triangles that tile the sphere, or more generally Euclidean plane or hyperbolic plane via their triangle group of reflections...

identities are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities involving...

triangle Regiomontanus Regiomontanus' angle maximization problem Reuschle's theorem Right triangle Routh's theorem Scalene triangle Schwarz triangle Schiffler's...

the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R , {\displaystyle f\colon U\to \mathbb...

Q={\sqrt {\frac {a_{1}^{2}+a_{2}^{2}+\cdots +a_{n}^{2}}{n}}}} The Cauchy–Schwarz inequality states that for all vectors u and v of an inner product space...

theorem Schwarzian derivative Schwarz triangle map Schwarz reflection principle Additive Schwarz method See his paper (Schwarz 1870b) See the paper (Mikhlin...

disphenoids are equilateral triangles, it can be constructed from a stretched triangular tiling net with four triangles in one direction and an even...

between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles...

contexts, the "(2,3,7) triangle group" most often refers, not to the full triangle group Δ(2,3,7) (the Coxeter group with Schwarz triangle (2,3,7) or a realization...

exhibit the triangle inequality property — or, more formally, the Schwarz inequality — and it violates the coincidence axiom. To repair the triangle inequality...

functions. Elliptic curve Schwarz–Christoffel mapping Carlson symmetric form Jacobi theta function Ramanujan theta function Dixon elliptic functions Abel...

of two solutions of the hypergeometric equation is also known as a Schwarz triangle map. The Picard–Fuchs equation can be cast into the form of Riemann's...

b with B and c with C. In other words, it is a symmetric function of the pair of triangles. Pedoe's inequality is a generalization of Weitzenböck's inequality...

analyze homomorphism densities is the Cauchy–Schwarz inequality. The effect of applying the Cauchy-Schwarz inequality is "folding" the graph over a line...

function of x . {\textstyle x.} log ⁡ ϕ ( x ) {\textstyle \log \phi (x)} is a convex function of log ⁡ ( x ) . {\textstyle \log(x).} Cauchy–Schwarz inequality –...

{sm} (0)=0} Or as the inverse of the Schwarz–Christoffel mapping from the complex unit disk to an equilateral triangle, the Abelian integral: z = ∫ 0 sm...

Charles Sanders Peirce in 1879. Each octant projects onto an isosceles right triangle, and these are arranged into a square. The name quincuncial refers to this...

every scalar s {\displaystyle s} and every function f . {\displaystyle f.} Absolute homogeneity, the triangle inequality, and non-negativity are the defining...