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Let J_nu(z) be a Bessel function of the first kind, Y_nu(z) a Bessel function of the second kind, and K_nu(z) a modified Bessel function of the first kind. Then ...

A generalization of the polylogarithm function defined by S_(n,p)(z)=((-1)^(n+p-1))/((n-1)!p!)int_0^1((lnt)^(n-1)[ln(1-zt)]^p)/tdt. The function reduces to the usual ...

Nielsen's spiral, also called the sici spiral (von Seggern 1993) is the spiral with parametric equations x(t) = aci(t) (1) y(t) = asi(t), (2) where ci(t) is the cosine ...

Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

If the Gauss map of a complete minimal surface omits a neighborhood of the sphere, then the surface is a plane. This was proven by Osserman (1959). Xavier (1981) subsequently ...

Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

A graphical plot which can be used for solving certain types of equations. According to Steinhaus (1999, p. 301), the Nomogram was invented by the French mathematicians ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...