Results 291 to 300 of about 3,569,062 (330)
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Special Functions of Mathematical Physics
1989Discussion of the most important formulae and construction of plots for some functions of mathematical physics relevant to quantum mechanics. These functions are Hermite polynomials, Legendre polynomials and Legendre functions, spherical harmonics, Bessel functions and spherical Bessel functions and Laguerre polynomials.
Siegmund Brandt +2 more
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2006
This is an overview article on q-special functions, a slightly extended version of an article to appear in the Encyclopedia of Mathematical Physics, Elsevier, 2006.
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This is an overview article on q-special functions, a slightly extended version of an article to appear in the Encyclopedia of Mathematical Physics, Elsevier, 2006.
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Special Functions and Approximations
2018The chapter contains the most important mathematical forumas that are used throughout the book. This collection should make the book self-contained. The chapter also contains some useful approximations that are used several times in the text.
Stefan Thurner +2 more
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A Knowledge Base on Special Functions
Journal of Mathematical Sciences, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. B. Yazik +6 more
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Special Functions in Geometric Function Theory
2005Conten t s Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 1. Gamma and beta functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 1.1. Functional equalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M. Vuorinen, S.-L. Qiu
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1969
Publisher Summary This chapter describes the different aspects of special functions. The general form of an ordinary linear differential equation of the second order with variable coefficients may be written for complex variables z and w as w′′ + p(z)w′ +q (z)w = 0.
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Publisher Summary This chapter describes the different aspects of special functions. The general form of an ordinary linear differential equation of the second order with variable coefficients may be written for complex variables z and w as w′′ + p(z)w′ +q (z)w = 0.
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1980
Publisher Summary This chapter discusses the special functions. A single-valued function f(z) of a complex variable, which is not a constant, is said to be elliptic if it has two periods 2ω1 and 2ω2. The ratio of the periods of an analytic function cannot be a real number.
I.S. Gradshteyn, I.M. Ryzhik
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Publisher Summary This chapter discusses the special functions. A single-valued function f(z) of a complex variable, which is not a constant, is said to be elliptic if it has two periods 2ω1 and 2ω2. The ratio of the periods of an analytic function cannot be a real number.
I.S. Gradshteyn, I.M. Ryzhik
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Special Functions of the Isomonodromy Type
Acta Applicandae Mathematica, 2000The purpose of this work is to describe a unified approach to special functions, using isomonodromy deformations. Roughly speaking, one considers linear systems of ordinary differential equations whose monodromies are independent of the position of the poles. Typically, the coefficients of such systems involve interesting special functions.
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2013
In this chapter are studied the properties of most of the important special functions of mathematical physics and chemistry. Some of these functions are obtained as solutions of differential equations of the type mentioned in the previous chapter, like Hermite, Laguerre, Legendre, hypergeometric and confluent hypergeometric functions, and different ...
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In this chapter are studied the properties of most of the important special functions of mathematical physics and chemistry. Some of these functions are obtained as solutions of differential equations of the type mentioned in the previous chapter, like Hermite, Laguerre, Legendre, hypergeometric and confluent hypergeometric functions, and different ...
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Composition and functions of bacterial membrane vesicles
Nature Reviews Microbiology, 2023Masanori Toyofuku +2 more
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