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Orthogonal Polynomials with the Prudnikov-Type Weights
Complex Analysis and Operator Theory ( IF 0.8 ) Pub Date : 2020-02-05 , DOI: 10.1007/s11785-019-00973-4
S. Yakubovich

New sequences of orthogonal polynomials with respect to the weight functions \(e^{-x} \rho _\nu (x),\ e^{- 1/x} x^{-1} \rho _{\nu } (x), \rho _{\nu }(x)= 2 x^{\nu /2} K_\nu (2\sqrt{x}),\ x >0, \nu \in {\mathbb {R}}\), where \(K_\nu (z)\) is the modified Bessel function, are investigated. The recurrence relations, explicit representations, generating functions and Rodrigues-type formulae are obtained.

中文翻译:

具有Prudnikov型权重的正交多项式

关于权重函数\(e ^ {-x} \ rho _ \ nu(x),\ e ^ {-1 / x} x ^ {-1} \ rho _ {\ nu}的正交多项式的新序列(x),\ rho _ {\ nu}(x)= 2 x ^ {\ nu / 2} K_ \ nu(2 \ sqrt {x}),\ x> 0,\ nu \ in {\ mathbb {R }} \),其中\(K_ \ nu(z)\)是修改后的Bessel函数。得到了递归关系,显式表示,生成函数和罗德里格斯型公式。
更新日期:2020-02-05
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