An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...

This paper considers the numerical simulation of incompressible viscous fluid flow in an infinite strip. A mixed spectral method is proposed using the Legendre approximation in one direction and the Legendre rational approximation in another direction. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Legendre-Legendre rational approximation are establishe...

Let ∆(x, n) = φ(x, n)−xφ(n)/n, where φ(x, n) is the Legendre totient function and φ(n) is the Euler totient function. An inequality for ∆(x, n) is known. In this paper we give a unitary analogue of this inequality, and more generally we give this inequality in the setting of regular convolutions.

Random regression test-day models using Legendre polynomials are commonly used for the estimation of genetic parameters and genetic evaluation for test-day milk production traits. However, some researchers have reported that these models present some undesirable properties such as the overestimation of variances at the edges of lactation. Describing genetic variation of saturated fatty acids ex...

We extend the Mason-Newman Lax pair for the elliptic complex MongeAmpère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. They imply the determining equation for symmetries of the complex Monge-Ampère equation as their differential compatibility condition. We shall identify the real and imagin...

We extend the Mason-Newman Lax pair for the elliptic complex MongeAmpère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. They imply the determining equation for symmetries of the complex Monge-Ampère equation as their differential compatibility condition. We shall identify the real and imagin...

It has recently been claimed that a Cardy-like limit of the superconformal index 4d N=4 SYM accounts for entropy function, whose Legendre transform corresponds to holographic dual AdS5 rotating black hole. Here we study this N=1 toric quiver gauge theories, observing corresponding function can be interpreted in terms data. Furthermore, some families models, compute comparing with similar result...

We show that the value function of an optimal stopping game driven by a one-dimensional diffusion can be characterised using the extension of the Legendre transform introduced in [19]. It is shown that under certain integrability conditions, a Nash equilibrium of the optimal stopping game can be derived from this extension of the Legendre transform. This result is an analytical complement to th...

A Table Errata is submitted concerning a formula in terms of a sum of two Gauss hypergeometric functions for the Ferrers function of the second kind (associated Legendre function of the second kind “on the cut”). This error occurs on p. 167 of Magnus, Oberhettinger & Soni (1966) Formulas and Theorems for the Special Functions of Mathematical Physics (third enlarged edition, Springer-Verlag, New...

Presented are the recurrence formulas to compute the derivatives of a general elliptic function, Weierstrass’s ℘ function, the Jacobian elliptic functions, and the incomplete elliptic integrals in the forms of Jacobi and Legendre with respect to the argument or the amplitude. The double precision computation by the formulas is correct with 15 digits or so for the first 10 orders of differentiat...