Dan DE handbook errata Fock

1 Hi Dan, 6 March 2011 While fumbling around with Mehler transforms, I think I sp otted an obscure errata in your Differential Equations book, 3rd Edition 1997. I don't see it in your websit e errata list last updated Nov 22, 2000. In Section 78 page 351 you have I think this is only correct for m = 0, but I don't have Sneddon' s book to check. However, right now I am staring at page 2 of F. Oberhettinger and T. P. Higgins, Tables of Lebedev, Mehler and Generalized Mehler Transforms , which is reference [21] on your page 355, and here is what I s ee: In something I wrote a while ago, I presented the transfor m in this manner: _______________________________________________________________________________ The generalized Mehler-Fock (Mehler-Fok) transform (Oberhet tinger and Higgins* page 2) is this, g(y) = ∫0 ∞ dτ P m -1/2+i τ(y) f( τ) // expansion f( τ) = ( τ/π) sh( πτ ) Γ(1/2-m+i τ) Γ(1/2-m-iτ) ∫1 ∞ dy Pm -1/2+i τ(y) g(y) // projection and for m = 0, using Γ(1/2+i τ)Γ(1/2-iτ) = π/cosh( πτ ), one obtains the regular Mehler-Fock transform, 2 g(y) = ∫0 ∞ dτ P -1/2+i τ(y) f( τ) // expansion f( τ) = τ th( πτ ) ∫1 ∞ dy P-1/2+i τ(y) g(y) // projection which can also be written as G( ξ) = ∫0 ∞ dτ P -1/2+i τ(ch ξ) f( τ) // expansion f( τ) = τ th( πτ ) ∫0 ∞ dξ sh ξ P-1/2+i τ(ch ξ) G( ξ) // projection * F. Oberhettinger and T. P. Higgins, Tables of Lebedev, Mehler and Generalized Mehler Transforms , (Boeing Scientific Research Laboratories, Mathematical N o. 246, 1961). A 48 page monograph with about 16 transforms per page. The first author is a member of A. Erdelyi et. al mentioned above. We obtained this book by interlibrary loan from the Coe library a t the University of Wyoming. _______________________________________________________________________________ As another piece of evidence, here is a clip from your page 355 Nas im reference [19] : You can set σ = 0 and t = ix to get something equivalent to Oberhettinger and Higgins. Best regards, Phil Lucht Salt Lake City