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The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

Tietze's graph is the cubic graph on 12 nodes and 18 edges illustrated above in a number of embeddings. It is implemented in the Wolfram Language as GraphData["TietzeGraph"]. ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k,m)(z) = ...

Analysis

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...