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 absolute value of the inner product between...

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...

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...

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...

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...

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...

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

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

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

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...

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...

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

properties of the lemniscate functions. This map was the first ever picture of a Schwarz–Christoffel mapping, in Schwarz (1869) p. 113. Schappacher (1997)...

The red triangle is a reclaimed symbol representing opposition to fascism and resistance to Nazi Germany's military occupation of Europe during World War...

Every triangle has a unique Steiner inellipse – an ellipse inside the triangle and tangent to the midpoints of the three sides of the triangle. The foci...

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 –...

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