In mathematics, the Chihara–Ismail polynomials are a family of
orthogonal polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
The most widely used orthogonal polynomials are the cl ...
introduced by , generalizing the van Doorn polynomials introduced by and the
Karlin–McGregor polynomials. They have a rather unusual
measure, which is
discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
*Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a ...
except for a single
limit point
In mathematics, a limit point, accumulation point, or cluster point of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also conta ...
at 0 with jump 0, and is non-symmetric, but whose support has an infinite number of both positive and negative points.
References
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Orthogonal polynomials
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