Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

Luo, Min-Jie; Raina, R. K.; Zhao, Shu-Han

doi:10.1080/10652469.2021.1958214

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Generating Function Formulas Related To the Associated Meixn...1

Concluding Remarks and Observations1

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2022

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Cited by 2 publications

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“…Generating functions related to this family of orthogonal polynomials arise in recent research [19][20][21]. Combining these expressions with our new parameter functions, we obtain the following generating function results:…”

Section: Generating Function Formulas Related To the Associated Meixn...mentioning

confidence: 85%

On the spherical clothoid

Ionut¹

2022

Preprint

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We revisit a nonlinear spline primitive for 3-space first studied by Even Mehlum. It is the spherical clothoid, the spherical curve with geodesic curvature a linear function of arc length. We present its Cartesian coordinate functions using confluent hypergeometric functions (the Kummer functions) and its stereographic projection onto the complex plane. New Humbert series results are also presented along with generating function formulas related to the associated Meixner-Pollaczek polynomials.

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Section: Generating Function Formulas Related To the Associated Meixn...mentioning

confidence: 85%

On the spherical clothoid

Ionut¹

2022

Preprint

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“…For the theory and applications of the various families of special functions and special polynomials, the interested reader should familiarize also with several other book and monographs such as [135][136][137][138][139][140][141][142][143][144][145][146][147][148]. Each of these books and monographs, together with some other recent developments (see [149][150][151][152][153]), as well as the hypergeometric functions of one and more variables studied in (for example) [154][155][156], will provide potential situations for the derivation and application of various families of generating functions.…”

Section: Concluding Remarks and Observationsmentioning

confidence: 99%

Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

Srivástava

2022

Mathematics

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In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions and hypergeometric polynomials in one, two and more variables. Many of the results as well as the methods and techniques used for their derivations, which are presented here, are intended to provide incentive and motivation for further research on the subject investigated in this article.

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Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

Cited by 2 publications

References 12 publications

On the spherical clothoid

On the spherical clothoid

Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

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