When I was introduced during my degree to special functions, I made friends with a number of nice functions - Laguerre, Legendre, Hermite, Bessel, and whatnot - but I made only a passing acquaintance with the hypergeometric and confluent hypergeometric functions, mostly limited to looking them up in Arfken and recoiling in horror at the dryness of the material and the lack of physical content in the calculations.

I know, of course, that this lack of physical content is also accompanied by an astounding generality. After a while I did get the core of the idea, which I believe is "explore all special functions whose series coefficients are rational functions of $n$", and I do find it appealing, but I've not had the energy nor the motivation to follow that up and see what's interesting about the thing.

However, it appears that the long-delayed moment is here and some pretty hairy integrals (think $\int_0^\infty x^k e^{-\alpha x^2}J_m(\beta x)dx$) have pushed some ugly "${}_1 F_1$" symbols onto my page. So my question is, then: **what's a good introduction to hypergeometric and confluent hypergeometric functions?** I'd like one where I can get an intuitive understanding of what to expect from them in different circumstances, what nice properties they have, and generally why it really *is* worth it to deal with them instead of their more specific cases like Laguerre, Legendre, Hermite, Bessel, etc.