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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.
Summary
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. Wolfram AI Course Assistant is available for this interactive course.
Featured Products & Technologies: Wolfram Language (available in Mathematica and Wolfram|One)
You'll Learn To
Make connections between differential equations and special functions as data structures
Perform asymptotic analysis and derive series expansions with mathematical rigor
Visualize special functions and their singularities in the complex plane
Analyze and apply gamma, Bessel, Airy, hypergeometric, elliptic, Heun, Meijer G, Fox H and many more functions
Solve physical and engineering problems using exact symbolic solutions (e.g. via DSolve)
Leverage orthogonal polynomials and special integrals in approximation theory and quantum mechanics
Summary
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. Wolfram AI Course Assistant is available for this interactive course.
Featured Products & Technologies: Wolfram Language (available in Mathematica and Wolfram|One)
You'll Learn To
Make connections between differential equations and special functions as data structures
Perform asymptotic analysis and derive series expansions with mathematical rigor
Visualize special functions and their singularities in the complex plane
Analyze and apply gamma, Bessel, Airy, hypergeometric, elliptic, Heun, Meijer G, Fox H and many more functions
Solve physical and engineering problems using exact symbolic solutions (e.g. via DSolve)
Leverage orthogonal polynomials and special integrals in approximation theory and quantum mechanics
