The use of fractional derivatives to expand analytical functions in terms of quadratic functions with applications to special functions

DOI10.1016/j.amc.2006.09.076zbMath1116.33001OpenAlexW2022110967MaRDI QIDQ884157

Richard Tremblay, Benoît-Jean Fugère

Publication date: 13 June 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.09.076

zbMATH Keywords

Taylor's theoremLaurent seriesSpecial functionsPower seriesFractional derivatives

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Power series (including lacunary series) in one complex variable (30B10) Hypergeometric functions (33C99)

Related Items

Numerical scheme for calculating of the fractional two-power relaxation laws in time-domain of measurements ⋮ Some relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol-type polynomials ⋮ Some relations involving a generalized fractional derivative operator ⋮ Remark on certain transformations for multiple hypergeometric functions ⋮ Taylor-like expansion in terms of a rational function obtained by means of fractional derivatives ⋮ A new Leibniz rule and its integral analogue for fractional derivatives ⋮ A new transformation formula for fractional derivatives with applications ⋮ Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus ⋮ New expansion formulas for a family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functions ⋮ Summation formulas obtained by means of the generalized chain rule for fractional derivatives ⋮ Further results involving a class of generalized Hurwitz-Lerch zeta functions

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