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JAT
2010
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13 years 2 months ago
Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures
Abstract: Inner products of the type f, g S = f, g ψ0 + f , g ψ1 , where one of the measures ψ0 or ψ1 is the measure associated with the Jacobi polynomials, are usually referre...
Eliana X. L. de Andrade, Cleonice F. Bracciali, La...
NA
2007
81views more  NA 2007»
13 years 3 months ago
Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials
In 2000, Reimer proved that a positive weight quadrature rule on the unit sphere Sd ⊂ Rd+1 has the property of quadrature regularity. Hesse and Sloan used a related property, ca...
Paul C. Leopardi
NA
2007
98views more  NA 2007»
13 years 3 months ago
Conjectured inequalities for Jacobi polynomials and their largest zeros
Inequalities are conjectured for the Jacobi polynomials P (α,β) n and their largest zeros. Special attention is given to the cases β = α − 1 and β = α. Key words. Jacobi po...
Walter Gautschi, Paul Leopardi
JAT
2007
103views more  JAT 2007»
13 years 3 months ago
Monotonicity of zeros of Jacobi polynomials
Denote by xn,k(α, β), k = 1, . . . , n, the zeros of the Jacobi polynomial P (α,β) n (x). It is well known that xn,k(α, β) are increasing functions of β and decreasing func...
Dimitar K. Dimitrov, Fernando R. Rafaeli