What is the Best Book for Understanding Transcendental Functions?

[logan3]

Is there a book that just goes over transcendental functions, from their introduction to advanced use? I'm looking for some more experience with thinking about the functions and gaining some insight into their deep relationships. Thank-you.

 

[SteamKing]

Which transcendental functions in particular?

 

[logan3]

All of them. But I'll take what I can get.

 

[marcusl]

Whittaker and Watson's "Modern Analysis" is a standard treatment. For even more depth, Erdelyi wrote a three volume set called "Higher Transcendental Functions" that is quite comprehensive.

 

[fourier jr]

i think lebedev had one also, on special functions

 

[dextercioby]

Special functions is a name given to the other functions than the so-called elementary ones. A direct connection to the <transcendental> attribute cannot be made, since there are elementary functions which are transcendental and special functions which are not (i.e. are algebraic, for example the orthogonal polynomials).

 

[fourier jr]

whoops, I thought they were just different names for the same class of functions

 

[dextercioby]

No, actually the subject of special functions is the part of mathematics I like most. Most of the known special functions are particular cases of general hypergeometric functions, especially Gauß ones.

As to the overall value, the 4th (latest, IIRC) edition of Whittaker & Watson should be the gem which would benefit the OP, so I 2nd the reccomendation.

 

[logan3]

Thank-you so much for the help. I think the Whittaker/Watson book looks very good. Thank-you.

 

[jasonRF]

Whittaker and Watson is now old enough that legal electronic copies can be found online for free:
http://www.e-booksdirectory.com/details.php?ebook=183

A reader for that book format can be found for free online (don't remember what it is called).

Note that some of the modern "cheap" printings of this book are terrible - they are literally printouts of this electronic copy (which has some pages that are not scanned well). I bought this one and immediately returned it:
https://www.amazon.com/dp/1438513909/?tag=pfamazon01-20

So if you want a hardcopy getting a used copy of an old printing seems to be the way to go. They can be found for cheap, too.

enjoy,

jason

 

[dextercioby]

<A reader for that book format can be found for free online (don't remember what it is called).>

One can find sources for downloading here http://djvu.org/resources/