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The Probability Integral

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Measure Integral And Probability

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Author : Marek Capinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Measure Integral And Probability written by Marek Capinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

The central concepts in this book are Lebesgue measure and the Lebesgue integral. Their role as standard fare in UK undergraduate mathematics courses is not wholly secure; yet they provide the principal model for the development of the abstract measure spaces which underpin modern probability theory, while the Lebesgue function spaces remain the main sour ce of examples on which to test the methods of functional analysis and its many applications, such as Fourier analysis and the theory of partial differential equations. It follows that not only budding analysts have need of a clear understanding of the construction and properties of measures and integrals, but also that those who wish to contribute seriously to the applications of analytical methods in a wide variety of areas of mathematics, physics, electronics, engineering and, most recently, finance, need to study the underlying theory with some care. We have found remarkably few texts in the current literature which aim explicitly to provide for these needs, at a level accessible to current under graduates. There are many good books on modern prob ability theory, and increasingly they recognize the need for a strong grounding in the tools we develop in this book, but all too often the treatment is either too advanced for an undergraduate audience or else somewhat perfunctory.

The Probability Integral

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Author : Paul J. Nahin
language : en
Publisher: Springer Nature
Release Date : 2023-09-08

The Probability Integral written by Paul J. Nahin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-08 with Science categories.

This book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.

The Probability Integral

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Author : William Fleetwood Sheppard
language : en
Publisher:
Release Date : 1966

The Probability Integral written by William Fleetwood Sheppard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Integrals categories.

Integration And Probability

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Author : Paul Malliavin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Integration And Probability written by Paul Malliavin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

It is a distinct pleasure to have the opportunity to introduce Professor Malliavin's book to the English-speaking mathematical world. In recent years there has been a noticeable retreat from the level of ab straction at which graduate-level courses in analysis were previously taught in the United States and elsewhere. In contrast to the practices used in the 1950s and 1960s, when great emphasis was placed on the most general context for integration and operator theory, we have recently witnessed an increased emphasis on detailed discussion of integration over Euclidean space and related problems in probability theory, harmonic analysis, and partial differential equations. Professor Malliavin is uniquely qualified to introduce the student to anal ysis with the proper mix of abstract theories and concrete problems. His mathematical career includes many notable contributions to harmonic anal ysis, complex analysis, and related problems in probability theory and par tial differential equations. Rather than developed as a thing-in-itself, the abstract approach serves as a context into which special models can be couched. For example, the general theory of integration is developed at an abstract level, and only then specialized to discuss the Lebesgue measure and integral on the real line. Another important area is the entire theory of probability, where we prefer to have the abstract model in mind, with no other specialization than total unit mass. Generally, we learn to work at an abstract level so that we can specialize when appropriate.

The Probability Integrals Of The Range And Of The Studentized Range

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Author : Harman Leon Harter
language : en
Publisher:
Release Date : 1959

The Probability Integrals Of The Range And Of The Studentized Range written by Harman Leon Harter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Analysis of variance categories.

The Probability Integrals Of The Range And Of The Studentized Range

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Author : Harmon Leon Harter
language : en
Publisher:
Release Date : 1959

The Probability Integrals Of The Range And Of The Studentized Range written by Harmon Leon Harter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Analysis of variance categories.

Evaluation Of The Probability Integral To High Precision

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Author : Francis Dominic Murnaghan
language : en
Publisher:
Release Date : 1965

Evaluation Of The Probability Integral To High Precision written by Francis Dominic Murnaghan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Probabilities categories.

The 'converging factor' for an asymptotic series representing a function f(x) is that number by which the (n + 1) term of the series must be multiplied so that the result of adding this product to the sum of the first n terms will be f(x). The determination to high precision of this factor for the asymptotic series representing the probability integral is described. Tables of this factor to 63 decimal places are included for n ranging from 2 to 64. (Author).