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1996, ISBN 9780471119630, xxvi, 717
Book
1989, ISBN 997150667X, xvi, 695
Book
1992, 2nd ed., ISBN 0070018480, xix, 479
Book
1996, ISBN 9780471113133, xii, 374
This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems... 
Functions, Special | Boundary value problems | Mathematical physics
Book
Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 350, pp. 326 - 342
We express a certain complex-valued solution of Legendre's differential equation as the product of an oscillatory exponential function and an integral involving only nonoscillatory elementary functions... 
Nonoscillatory phase functions | Fast algorithms | Special functions | NODES | GAUSS-LEGENDRE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EXPANSIONS | WEIGHTS | COMPUTATION | PHYSICS, MATHEMATICAL | Differential equations | Computer science | Algorithms | DIFFERENTIAL EQUATIONS | LEGENDRE POLYNOMIALS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ASYMPTOTIC SOLUTIONS
Journal Article
Review of scientific instruments, ISSN 1089-7623, 2004, Volume 75, Issue 11, pp. 4989 - 4996
We present an inversion method called pBasex aimed at reconstructing the original Newton sphere of expanding charged particles from its two-dimensional projection by fitting a set of basis functions... 
PHOTOIONIZATION | INSTRUMENTS & INSTRUMENTATION | PHYSICS, APPLIED | CIRCULAR-DICHROISM | ANGULAR-DISTRIBUTION | PRODUCTS | PHOTOELECTRON | IONS | EMISSION | IONIZATION | MOLECULES | LEGENDRE POLYNOMIALS | IMAGE PROCESSING | PHOTOELECTRON SPECTROSCOPY | SPATIAL RESOLUTION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IMAGES | CHARGED PARTICLES | PERFORMANCE | NOISE | ALGORITHMS | ACCURACY
Journal Article
Journal of dynamic systems, measurement, and control, ISSN 1528-9028, 2018, Volume 140, Issue 1
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 477, Issue 2, pp. 1328 - 1352
... of binomial coefficients and the Franel numbers by means of suitable generating functions and hypergeometric function... 
Franel numbers | Bernoulli and Euler numbers and polynomials | Mirimanoff polynomial | Legendre polynomial | p-adic integrals | Generating functions | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | IDENTITIES | Francl numbers | EULER NUMBERS | MATHEMATICS | ZETA | RECURRENCES | PRODUCTS
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 03/2014, Volume 101, Issue 3, pp. 303 - 329
.... In the present paper, we study the Riemannian distance function associated with the Heston model and obtain explicit formulas for this function using geometrical and analytical methods... 
Grushin plane | Legendre–Fenchel transform | Limiting cumulant generating function | Heston model | Legendre-Fenchel transform | MATHEMATICS | MATHEMATICS, APPLIED | IMPLIED VOLATILITY | MODEL | EQUATION
Journal Article
1966, 1st English ed., Mathematical tables series, v. 40, 107
Book
Boletim da Sociedade Paranaense de Matematica, ISSN 0037-8712, 2018, Volume 36, Issue 1, pp. 177 - 193
In the present work we derive various integral formulas involving ℵ-function multiplied with algebraic functions and special functions. 
Jacobi polynomials | H-function | Bessel Maitland function | I-function | Aleph function | Hypergeometric function | Legendre function
Journal Article
Journal of Machine Learning Research, ISSN 1532-4435, 09/2010, Volume 11, pp. 2423 - 2455
In this paper, we propose a general framework for sparse semi-supervised learning, which concerns using a small portion of unlabeled data and a few labeled data to represent target functions and thus... 
Multi-view regularization | Representer theorem | Statistical learning theory | Fenchel-Legendre conjugate | Support vector machine | Semi-supervised learning | support vector machine | representer theorem | multiview regularization | statistical learning theory | semi-supervised learning | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Journal Article
Journal of Mathematical Chemistry, ISSN 0259-9791, 3/2018, Volume 56, Issue 3, pp. 825 - 849
... . We first construct an associated Legendre function expression for eigenfunctions of the Laplacian and use superposition principle to get a solution for the Laplace equation on $$\mathbf {H}^{n}$$ Hn... 
33C45 | 35J05 | 35K15 | 35P10 | 44A20 | 47A10 | Hyperbolic upper half-space | 44A15 | Theoretical and Computational Chemistry | Poisson kernel | Chemistry | Physical Chemistry | Poincaré unit ball | Special functions | Associated Legendre function | Math. Applications in Chemistry | 42C05 | Poincare unit ball | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EIGENFUNCTIONS | CHEMISTRY, MULTIDISCIPLINARY | Functions, Exponential | Analysis | Poisson processes
Journal Article
Annals of Physics, ISSN 0003-4916, 06/2013, Volume 333, pp. 90 - 103
... to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2... 
Square-integrable function | Special function | Lie algebra | PHYSICS, MULTIDISCIPLINARY | Algebra | LEGENDRE POLYNOMIALS | SPACE | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | LIE GROUPS | HARMONICS | SPHERICAL HARMONICS | IRREDUCIBLE REPRESENTATIONS
Journal Article
Journal of Vibration and Control, ISSN 1077-5463, 11/2018, Volume 24, Issue 21, pp. 5030 - 5043
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 12, pp. e103 - e108
We will solve the inhomogeneous Legendre’s differential equation and apply this result to estimate the error bound occurring when an analytic function... 
Legendre function | Analytic function | Approximation | Legendre’s differential equation | Legendre's differential equation | MATHEMATICS | MATHEMATICS, APPLIED | Error analysis | Analytic functions | Mathematical analysis | Differential equations | Legendre functions | Nonlinearity | Estimates
Journal Article
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