Results 101 to 110 of about 53,695 (215)

Notes on Legendre polynomials [PDF]

Bulletin of the American Mathematical Society, 1945
Not ...
openaire   +3 more sources

Congruences concerning Legendre polynomials [PDF]

Proceedings of the American Mathematical Society, 2010
Let $p$ be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for $\sum_{k=0}^{\frac{p-1}2}\binom{2k}k^2m^{-k}\mod {p^2}$. In particular, we confirm several conjectures of Z.W. Sun. We also pose 13 conjectures on supercongruences.
openaire   +3 more sources

Sums of three positive cubes

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
wiley   +1 more source

Combinatorial interpretations of the Jacobi-Stirling numbers

, 2009
The Jacobi-Stirling numbers of the first and second kinds were introduced in 2006 in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers.
Gelineau, Yoann, Zeng, Jiang
core   +1 more source

On the non-existence of some interpolatory polynomials

International Journal of Mathematics and Mathematical Sciences, 1986
Here we prove that if xk, k=1,2,…,n+2 are the zeros of (1−x2)Tn(x) where Tn(x) is the Tchebycheff polynomial of first kind of degree n, αj, βj, j=1,2,…,n+2 and γj, j=1,2,…,n+1 are any real numbers there does not exist a unique polynomial Q3n+3(x) of ...
C. H. Anderson, J. Prasad
doaj   +1 more source

Oceanic Mesoscale Eddy Fitting Using Legendre Polynomial Surface Fitting Model Based on Along-Track Sea Level Anomaly Data

Remote Sensing
Exploring the spatial distribution of sea surface height involves two primary methodologies: utilizing gridded reanalysis data post-secondary processing or conducting direct fitting along-track data.
Chunzheng Kong, Yibo Zhang, Jie Shi, Xianqing Lv   +3 more
doaj   +1 more source

On the number of zeros of iterated operators on analytic Legendre expansions

International Journal of Mathematics and Mathematical Sciences, 2001
Let L=(1−z2)D2−2zD, D=d/dz and f(z)=∑n=0∞cnpn(z), with Pn being the nth Legendre polynomial and f analytic in an ellipse with foci ±1. Set Lk=L(Lk−1), k≥2. Then the number of zeros of Lkf(z) in this ellipse is O(klnk).
Carl Prather
doaj   +1 more source

Two legendre polynomial identities [PDF]

, 1983
Rawlins, AD
core   +1 more source

Analysis of Faceted Gratings Using C-Method and Polynomial Expansion

Photonics
The coordinate-transformation-based differential method developed by Chandezon et al. is recognized as one of the simplest and most versatile approaches for modeling surface-relief gratings.
Gérard Granet, Kofi Edee
doaj   +1 more source

Two-Dimensional Legendre Polynomial Method for Internal Tide Signal Extraction

Remote Sensing
This study employs the two-dimensional Legendre polynomial fitting (2-D LPF) method to fit M2 tidal harmonic constants from satellite altimetry data within the region of 53°E–131°E, 34°S–6°N, extracting internal tide signals acting on the sea surface ...
Yunfei Zhang, Cheng Luo, Haibo Chen, Wei Cui, Xianqing Lv   +4 more
doaj   +1 more source