# How can I learn special functions and differential equation

• Karmerlo
In summary, Legendre Functions, Spherical Harmonic Functions, Bessel Functions, Neumann Functions, Airy Functions, Confluent Hypergeometric Functions, Laguerre Functions, and Hermitte Functions are complex topics with wide applications in physics. Despite the difficulty in learning them, there are valuable reference books available, such as "Handbook of Mathematical Functions" and "An Atlas of Functions". Additionally, for French readers, "Safari au pays des fonctions spéciales" provides a comprehensive guide to special functions with a bibliography and summary of the most useful ones.
Karmerlo
Legendre Functions, Spherical Harmonic Functions, Bessel Functions, Neumann Functions, Airy Functions, Confluent Hypergeometric Functions, Laguerre Functions, Hermitte Functions...

I find this learning is so tedious, traumatic, and miserable. I find it so difficult to manage.
But I have to manage it, since there are wide applications in physics (Electrodynamics,Quantum Mechanics, when working on various sorts of ordinary/partial differential equation, when working on moment expansion) of such "good stuffs".

Do anyone have some very good reference (easy to find in campus lib.) can help me learn this?

Or any good suggestions to do this?
Thanks.

Hi !
I suggest two very valuable books :

M.Abramowitz, I.A.Stegun, "Handbook of Mathematical Functions", Dover Publications, N.-Y., 1972

J.Spanier, K.B.Oldham, "An Atlas of Functions", Hemisphere Pubishing Corporation, Springer-Verlag, 1987. (There is a more recent edition)

For French readers, a compendium about the use of special functions :
"Safari au pays des fonctions spéciales"
http://www.scribd.com/JJacquelin/documents
A bibliography is provided page 11 and a summary of the most usefull special functions pp.12-17

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## 1. How important is it to learn special functions and differential equations as a scientist?

Learning special functions and differential equations is crucial for scientists, as they play a key role in modeling and understanding various natural phenomena. These mathematical tools are used extensively in fields such as physics, engineering, and biology to describe and solve complex problems.

## 2. What are some common special functions and differential equations that scientists encounter?

Some commonly used special functions in science include trigonometric functions, exponential and logarithmic functions, and Bessel functions. Differential equations, on the other hand, can range from simple linear equations to more complex non-linear equations such as the Navier-Stokes equations.

## 3. How can I improve my understanding of special functions and differential equations?

To improve your understanding of special functions and differential equations, it is important to have a strong foundation in calculus and algebra. You can also practice solving different types of equations and familiarize yourself with the properties and applications of various special functions.

## 4. Are there any resources available to help me learn special functions and differential equations?

Yes, there are many resources available to help you learn special functions and differential equations. You can refer to textbooks, online lectures and tutorials, and practice problems. Additionally, seeking guidance from a mentor or tutor can also be beneficial.

## 5. How can I apply my knowledge of special functions and differential equations in my research or work?

Special functions and differential equations are powerful tools that can be applied in various areas of research and work. Scientists use them to model and analyze data, predict future trends, and solve complex problems in their respective fields. With a solid understanding of these mathematical concepts, you can enhance your research and contribute to new discoveries and advancements.

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