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Hace 4 días · The Legendre symbol is a function that encodes the information about whether a number is a quadratic residue modulo an odd prime. It is used in the law of quadratic reciprocity to simplify notation.
Hace 2 días · The eigenfunction corresponding to eigenvalues λ n = n(n+1), n = 0, 1, 2, …, are convensionally called associated Legendre functions. They usually are denoted by \( P_n^m (x) , \quad m=0,1,2,\ldots , n; \) or by P n ( m , x ).
1 de jul. de 2024 · Legendre Identity -- from Wolfram MathWorld. Calculus and Analysis. Special Functions. Elliptic Integrals.
18 de jun. de 2024 · This paper considers some aspects of Legendre’s conjecture as a conjecture and estimates the number of primes in some intervals in order to portray a compelling picture of some of the computational issues generated by the conjecture.
29 de jun. de 2024 · See. Legendre Function of the Second Kind. About MathWorld; MathWorld Classroom; Contribute; MathWorld Book; wolfram.com; 13,195 Entries
Hace 2 días · The ordinary generating function for Legendre polynomials is \begin{equation} \label{EqLege1.1} G(x,t) = \frac{1}{\sqrt{1 -2xt + t^2}} = \sum_{n\ge 0} P_n (x)\, t^n , \end{equation} where P n ( x is the Legendre polynomial of degree n .
Hace 6 días · Introduction to Linear Algebra with Mathematica. Glossary. Preface. Legendre polynomials are eigenfunctions corresponding to eigenvalues λ = n ( n +1) of the singular Sturm--Liouville problem, (1 − x2)y ″ − 2xy. + λy = 0, x ∈ ( − 1, 1), y( ± 1) < ∞, where n ∈ ℕ = {0, 1, 2, …} is a nonnegative integer.
