Ebook: Special Functions for Applied Scientists

Special Functions for Applied Scientists provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at the PhD level and covers a wide-array of topics and begins by introducing elementary classical special functions. From there, differential equations and some applications into statistical distribution theory are examined.

The fractional calculus chapter covers fractional integrals and fractional derivatives as well as their applications to reaction-diffusion problems in physics, input-output analysis, Mittag-Leffler stochastic processes and related topics. The authors then cover q-hypergeometric functions, Ramanujan's work and Lie groups.

The latter half of this volume presents applications into stochastic processes, random variables, Mittag-Leffler processes, density estimation, order statistics, and problems in astrophysics.

Professor Dr. A.M. Mathai is Emeritus Professor of Mathematics and Statistics, McGill University, Canada.

Professor Dr. Hans J. Haubold is an astrophysicist and chief scientist at the Office of Outer Space Affairs of the United Nations.

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Special Functions for Applied Scientists provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at the PhD level and covers a wide-array of topics and begins by introducing elementary classical special functions. From there, differential equations and some applications into statistical distribution theory are examined.

The fractional calculus chapter covers fractional integrals and fractional derivatives as well as their applications to reaction-diffusion problems in physics, input-output analysis, Mittag-Leffler stochastic processes and related topics. The authors then cover q-hypergeometric functions, Ramanujan's work and Lie groups.

The latter half of this volume presents applications into stochastic processes, random variables, Mittag-Leffler processes, density estimation, order statistics, and problems in astrophysics.

Professor Dr. A.M. Mathai is Emeritus Professor of Mathematics and Statistics, McGill University, Canada.

Professor Dr. Hans J. Haubold is an astrophysicist and chief scientist at the Office of Outer Space Affairs of the United Nations.

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Special Functions for Applied Scientists provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at the PhD level and covers a wide-array of topics and begins by introducing elementary classical special functions. From there, differential equations and some applications into statistical distribution theory are examined.

The fractional calculus chapter covers fractional integrals and fractional derivatives as well as their applications to reaction-diffusion problems in physics, input-output analysis, Mittag-Leffler stochastic processes and related topics. The authors then cover q-hypergeometric functions, Ramanujan's work and Lie groups.

The latter half of this volume presents applications into stochastic processes, random variables, Mittag-Leffler processes, density estimation, order statistics, and problems in astrophysics.

Professor Dr. A.M. Mathai is Emeritus Professor of Mathematics and Statistics, McGill University, Canada.

Professor Dr. Hans J. Haubold is an astrophysicist and chief scientist at the Office of Outer Space Affairs of the United Nations.

Content:
Front Matter....Pages i-xxv
Basic Ideas of Special Functions and Statistical Distributions....Pages 1-78
Mittag-Leffler Functions and Fractional Calculus....Pages 79-134
An Introduction to q-Series....Pages 135-157
Ramanujan's Theories of Theta and Elliptic Functions....Pages 159-209
Lie Group and Special Functions....Pages 211-245
Applications to Stochastic Process and Time Series....Pages 247-295
Applications to Density Estimation....Pages 297-309
Applications to Order Statistics....Pages 311-340
Applications to Astrophysics Problems....Pages 341-387
An Introduction to Wavelet Analysis....Pages 389-408
Jacobians of Matrix Transformations....Pages 409-428
Special Functions of Matrix Argument....Pages 429-455
Back Matter....Pages 457-464

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Special Functions for Applied Scientists provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at the PhD level and covers a wide-array of topics and begins by introducing elementary classical special functions. From there, differential equations and some applications into statistical distribution theory are examined.

The fractional calculus chapter covers fractional integrals and fractional derivatives as well as their applications to reaction-diffusion problems in physics, input-output analysis, Mittag-Leffler stochastic processes and related topics. The authors then cover q-hypergeometric functions, Ramanujan's work and Lie groups.

The latter half of this volume presents applications into stochastic processes, random variables, Mittag-Leffler processes, density estimation, order statistics, and problems in astrophysics.

Professor Dr. A.M. Mathai is Emeritus Professor of Mathematics and Statistics, McGill University, Canada.

Professor Dr. Hans J. Haubold is an astrophysicist and chief scientist at the Office of Outer Space Affairs of the United Nations.

Content:
Front Matter....Pages i-xxv
Basic Ideas of Special Functions and Statistical Distributions....Pages 1-78
Mittag-Leffler Functions and Fractional Calculus....Pages 79-134
An Introduction to q-Series....Pages 135-157
Ramanujan's Theories of Theta and Elliptic Functions....Pages 159-209
Lie Group and Special Functions....Pages 211-245
Applications to Stochastic Process and Time Series....Pages 247-295
Applications to Density Estimation....Pages 297-309
Applications to Order Statistics....Pages 311-340
Applications to Astrophysics Problems....Pages 341-387
An Introduction to Wavelet Analysis....Pages 389-408
Jacobians of Matrix Transformations....Pages 409-428
Special Functions of Matrix Argument....Pages 429-455
Back Matter....Pages 457-464
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