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Harmonic generalized functions in generalized function algebras
Monatshefte für Mathematik, 2009We investigate basic properties of harmonic generalized functions within the framework of J. F. Colombeau’s theory of generalized functions. In particular, we present various theorems concerning the Maximum principle, Liouville’s theorem, singularities and Poisson formula.
Pilipović, Stevan +1 more
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Journal of Applied Probability, 1982
There are described in the literature many spaces of what are variously described as generalized functions, distributions, or improper functions. This article introduces another. The new space is like that of M. J. Lighthill in containing the Fourier transform of every element and in having a particularly simple theory of trigonometric and Fourier ...
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There are described in the literature many spaces of what are variously described as generalized functions, distributions, or improper functions. This article introduces another. The new space is like that of M. J. Lighthill in containing the Fourier transform of every element and in having a particularly simple theory of trigonometric and Fourier ...
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Generating functions for the generalized Gauss hypergeometric functions
Applied Mathematics and Computation, 2014Formulas and identities involving many well-known special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) play important roles in themselves and in their diverse applications. Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim
Shilpi Jain +2 more
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1998
Abstract In this chapter, we are going to present a useful calculation technique. The basic idea, quite a surprising one, is to consider an infinite sequence of real numbers and associate a certain continuous function with it, the so-called generating function of the sequence.
Jirří Matoušek, Jaroslav Nešetřil
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Abstract In this chapter, we are going to present a useful calculation technique. The basic idea, quite a surprising one, is to consider an infinite sequence of real numbers and associate a certain continuous function with it, the so-called generating function of the sequence.
Jirří Matoušek, Jaroslav Nešetřil
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Il Nuovo Cimento B Series 11, 1992
We present an algebraic method to obtain expansions and generating functions for the product of two hypergeometric functions. Applications are discussed.
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We present an algebraic method to obtain expansions and generating functions for the product of two hypergeometric functions. Applications are discussed.
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Generating Functions and Characteristic Functions
1992These functions are of considerable use in theoretical probability, i.e., proving probability theorems. They are also of use to us when we wish to put two distributions together. Consider x = x 1 + x 2 + ... + x n, where x 1 is distributed according to one distribution, x 2 according to another, etc.
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Neophobia: generality and function
Behavioral and Neural Biology, 1981The hypothesis that neophobia varies directly with the flavor of toxic substances in the natural habitat of a species, and possibly also with the flavors of necessary nutrients in the natural habitat is examined in eight experiments using rats, guinea pigs, and gerbils. Neophobia was found to be an inverted U-shaped function of concentration.
Arnold D. Holzman, Ralph R. Miller
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Instruments and Experimental Techniques, 2004
A synchronizing generator of triangular, sine-wave, and rectangular signals with variable frequencies and amplitudes is described. The main generator of triangular signals is complemented with a functional converter to obtain a sine function using the piecewise-linear approximation.
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A synchronizing generator of triangular, sine-wave, and rectangular signals with variable frequencies and amplitudes is described. The main generator of triangular signals is complemented with a functional converter to obtain a sine function using the piecewise-linear approximation.
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Generating Functions and Partitions
1984The generating functions introduced in Chap. 20 and defined by Dirichlet series are not the only kind of generating functions. Here we shall briefly get to know another type of generating function with many useful properties that are applicable in numerous fields of mathematics and other sciences.
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1960
Let {a n , n≧0} be a sequence of real numbers. Its generating function is the power series $$A\left( u \right)=\sum\limits_{n=0}^{\infty }{{{a}_{n}}}{{u}^{n}}$$ provided that it has a nonvanishing radius of convergence. In particular if the a n are probabilities then the radius of convergence is at least equal to one.
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Let {a n , n≧0} be a sequence of real numbers. Its generating function is the power series $$A\left( u \right)=\sum\limits_{n=0}^{\infty }{{{a}_{n}}}{{u}^{n}}$$ provided that it has a nonvanishing radius of convergence. In particular if the a n are probabilities then the radius of convergence is at least equal to one.
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