Results 21 to 30 of about 155,769 (214)

Generalized Legendre Polynomials

Journal of Mathematical Analysis and Applications, 1993
Let \((\lambda_ n)_{n\in\mathbb{N}}\) be a sequence of distinct real numbers with \(\lambda_ n>-1/2\). The authors orthogonalize the functions \(\{x^{\lambda_ 1},x^{\lambda_ 2},\dots\}\) with respect to the inner product \(\langle f,g\rangle:=\int_ 0^ 1 f(x)g(x)dx\) by using Gram-Schmidt-orthogonalization.
Mccarthy, P.C., Sayre, J.E., Shawyer, B.L.R.   +2 more
openaire   +2 more sources

Certain integrals involving generalized Mittag-Leffler type functions

Vojnotehnički Glasnik, 2022
Introduction/purpose: Certain integrals involving the generalized MittagLeffler function with different types of polynomials are established. Methods: The properties of the generalized Mittag-Leffler function are used in conjunction with different ...
Sirazul Haq, Maggie Aphane, Mohammad Saeed Khan, Nicola Fabiano   +3 more
doaj   +1 more source

Some results for sums of products of Chebyshev and Legendre polynomials

Advances in Difference Equations, 2019
In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials.
Yuan He
doaj   +1 more source

Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations

Journal of Mathematics, 2022
In this work, we apply the operational matrix based on shifted Legendre polynomials for solving Prabhakar fractional differential equations. The Prabhakar derivative is defined in three-parameter Mittag-Leffler function. We achieve this by first deriving
Farah Suraya Md Nasrudin, Chang Phang
doaj   +1 more source

RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS

Проблемы анализа, 2020
We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
doaj   +1 more source

Polynomials to model the growth of young bulls in performance tests

Animal, 2014
The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied.
D.C.B. Scalez, B.O. Fragomeni, T.L. Passafaro, I.G. Pereira, F.L.B. Toral   +4 more
doaj   +1 more source

Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function

Abstract and Applied Analysis, 2014
The family of nth order q-Legendre polynomials are introduced. They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the ...
David W. Pravica, Njinasoa Randriampiry, Michael J. Spurr   +2 more
doaj   +1 more source

Genetic Evaluation for Functional Longevity in Nellore Cattle. [PDF]

J Anim Breed Genet
ABSTRACT Stayability (STAY) presents limitations in capturing genetic variability among animals with varying calving records up to 76 months of age. Furthermore, because STAY is measured late in life (typically at 6 years of age), it inherently prolongs generation intervals.
Fernandes GSS, Dos Santos DR, Boligon AA, Santana ML, Menezes GRO, Ayres DR, Bignardi AB, Pereira RJ.   +7 more
europepmc   +2 more sources

Omnidirectional Interaction Networks Modulating Phenotypic Plasticity in the Gut Microbiota Towards Ulcerative Colitis

Advanced Science, EarlyView.
This study employs a spouse‐pair cohort design and an idopNetwork model that integrates evolutionary game theory, predator‐prey dynamics, and developmental modularity theory to reconstruct maximally informative microbial interaction networks. This approach reveals how interspecies interactions drive the phenotypic plasticity of the gut microbiota in ...
Huizhen Li, Jiayi Li, Ang Dong, Xiaoyan Guo, Qiuyue Tu, Zelin Feng, Haojia Lin, Yanru Zhang, Yuxuan Hao, Huiying Gong, Yihan Meng, Yu Wang, Shing‐Tung Yau, Xiaocang Cao, Rongling Wu, Xinjuan Liu   +15 more
wiley   +1 more source

Enhanced High Dimensionality and the Information Processing Capacity in Interfered Spin Wave‐Based Reservoir Computing, Achieved With Eight Detectors

Advanced Electronic Materials, EarlyView.
Physical reservoir computing (PRC) based on spin wave interference has demonstrated high computational performance, yet room for improvement remains. In this study, we fabricated this concept PRC with eight detectors and evaluated the impact of the number of detectors using a chaotic time series prediction task.
Sota Hikasa, Wataru Namiki, Daiki Nishioka, Maki Nishimura, Ryo Iguchi, Kazuya Terabe, Takashi Tsuchiya   +6 more
wiley   +1 more source