Symbolic computations via Fourier–Legendre expansions and fractional operators

DOI10.1080/10652469.2021.1919103zbMath1501.33003OpenAlexW3181323051MaRDI QIDQ5029049

Marco Cantarini, Jacopo D'Aurizio, John Maxwell Campbell

Publication date: 11 February 2022

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2021.1919103

zbMATH Keywords

fractional calculushypergeometric functionclosed formFourier-Legendre expansion

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Generalized hypergeometric series, ({}_pF_q) (33C20) Numerical approximation and evaluation of special functions (33F05)

Related Items (5)

A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series ⋮ A series evaluation technique based on a modified Abel lemma ⋮ Applications of Caputo operators in the evaluation of Clebsch–Gordan-type multiple elliptic integrals ⋮ New Clebsch–Gordan‐type integrals involving threefold products of complete elliptic integrals ⋮ Lemniscate-like constants and infinite series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(q\)-fractional calculus and equations
• A generalization of Clausen's identity
• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• Hypergeometric transformation formulas of degrees 3, 7, 11 and 23
• On the Cesàro average of the numbers that can be written as sum of a prime and two squares of primes
• Three-term relations for \(_3F_2(1)\)
• Surprising identities for the hypergeometric \({}_{4}F_{3}\) function
• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
• Fractional calculus via Laplace transform and its application in relaxation processes
• Harmonic number identities via the Newton-Andrews method
• New series involving harmonic numbers and squared central binomial coefficients
• Some identities involving the Cesàro average of the Goldbach numbers
• On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
• A Cesàro average of Goldbach numbers
• Series containing squared central binomial coefficients and alternating harmonic numbers
• Fractional Derivatives and Special Functions
• Euler Sums and Contour Integral Representations
• On the Cesàro average of the “Linnik numbers”
• Closed Forms: What They Are and Why We Care
• A Further Extension of the Leibniz Rule to Fractional Derivatives and Its Relation to Parseval’s Formula

This page was built for publication: Symbolic computations via Fourier–Legendre expansions and fractional operators