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On the Expansion of Legendre Polynomials in Bicomplex Space and Coupling with Fractional Operators
AxiomsIn this paper, we introduce a novel version of the Legendre polynomials in the bicomplex system. We investigate the essential properties of the Legendre polynomial, focusing on its bicomplex structure, generating functions, orthogonality, and recurrence ...
Ahmed Bakhet +3 more
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On some integrals over the product of three Legendre functions [PDF]
, 2013 The definite integrals $\int_{-1}^{1}(1-x^{2})^{(\nu-1)/2}[P_{\nu}(x)]^{3}\, \mathrm{d}x$, $\int_{-1}^{1}(1-x^{2})^{(\nu-1)/2} [P_{\nu}(x)]^{2}P_{\nu}(-x)\, \mathrm{d}x$, $\int_{-1}^{1}x(1-x^{2})^{(\nu-1)/2}[P_{\nu+1}(x)]^{3}\,\mathrm{d}x$, and $\int_{-1}
Yajun Zhou
semanticscholar +1 more source
Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.This review aims to provide a broad understanding for interdisciplinary researchers in engineering and clinical applications. It addresses the development and control of magnetic actuation systems (MASs) in clinical surgeries and their revolutionary effects in multiple clinical applications.
Yingxin Huo +3 more
wiley +1 more source
On the Numerical Evaluation of Legendre's Chi-Function [PDF]
Mathematics of Computation, 1992 Legendre’s chi-function, χ
Boersma, J., Dempsey, J.P.
openaire +3 more sources
The Anatomical Record, EarlyView.Abstract A recent debate has emerged between Caspar et al. (2024) and Herculano‐Houzel (2023) on inferring extinct dinosaur cognition by estimating brain neuron counts. While thought‐provoking, the discussion largely overlooks the function of cognition, as well as partly neglects the difficulties involved in estimating neuron numbers, which according ...
Thomas Rejsenhus Jensen +7 more
wiley +1 more source
Lactation curve modelling using Legendre Polynomial in Sahiwal cattle
Indian Journal of Animal Sciences, 2016 Present study aimed at modelling lactation curve in Sahiwal cattle using normalized Legendre polynomials functions of standardized units of time and understanding the variation of lactation curve in different lactations. Among the first three lactations,
VED PRAKASH +3 more
doaj +1 more source
The Anatomical Record, EarlyView.Abstract Last year, we challenged the view that large‐bodied theropod dinosaurs such as Tyrannosaurus rex resembled primates in cognition and behavior, a proposition made by Herculano‐Houzel in 2023. More recently, Jensen et al. have criticized our work on this topic, raising methodological and conceptual issues.
Kai R. Caspar +5 more
wiley +1 more source
Advances in Meteorology, 2017 Chebyshev and Legendre polynomial expansion is used to reconstruct the Henyey-Greenstein phase function and the phase functions of spherical and nonspherical particles.
Feng Zhang +4 more
doaj +1 more source
Osteohistology of two phorusrhacids reveals uninterrupted growth strategy
The Anatomical Record, EarlyView.Abstract Phorusrhacidae were apex predators that primarily dominated South America ecosystems for at least 40 million years with their imposing size and predatory lifestyle—yet some aspects of their biology remain poorly understood. Osteohistology is a tool for understanding growth dynamics and biomechanical adaptations.
Lotta Dreyer +2 more
wiley +1 more source
, 2014 A formulation of the fractional Legendre functions is constructed to solve the generalized time-fractional diffusion equation. The fractional derivative is described in the Caputo sense.
M. Syam, M. Al-Refai
semanticscholar +1 more source