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Intro to special functions, properties and applications using Wolfram Language. Learn foundational methods, gamma and zeta families, special integrals, Bessel and Airy functions, orthogonal polynomials and hypergeometric functions, plus advanced topics.
This course offers a comprehensive introduction to special functions, their properties and their wide-ranging applications through the powerful lens of Wolfram Language. The course begins with the historical development of special functions and foundational methods for working with them, including symbolic evaluation, analytic continuation and high-precision numerical computation. Various exercises help you deepen your knowledge and fundamental understanding of the topic. As the lessons progress, you'll explore major classes of special functions, including the gamma and zeta families, special integrals, Bessel and Airy functions, orthogonal polynomials and hypergeometric functions. Advanced topics include elliptic and Heun-related functions, multivariate generalizations like the Appell functions and superfunctions such as Meijer G and Fox H. These topics, though essential in many areas of mathematics, physics and engineering, are often underrepresented in traditional university curricula. This course was designed to fill that gap with practical computation, visualization and theory. A free ebook version of this material is available as part of the Wolfram eTextbook Series. Wolfram AI Course Assistant is available for this interactive course.
This course offers a comprehensive introduction to special functions, their properties and their wide-ranging applications through the powerful lens of Wolfram Language. The course begins with the historical development of special functions and foundational methods for working with them, including symbolic evaluation, analytic continuation and high-precision numerical computation. Various exercises help you deepen your knowledge and fundamental understanding of the topic. As the lessons progress, you'll explore major classes of special functions, including the gamma and zeta families, special integrals, Bessel and Airy functions, orthogonal polynomials and hypergeometric functions. Advanced topics include elliptic and Heun-related functions, multivariate generalizations like the Appell functions and superfunctions such as Meijer G and Fox H. These topics, though essential in many areas of mathematics, physics and engineering, are often underrepresented in traditional university curricula. This course was designed to fill that gap with practical computation, visualization and theory. A free ebook version of this material is available as part of the Wolfram eTextbook Series. Wolfram AI Course Assistant is available for this interactive course.
