Dan DE handbook errata Fock

Hi Dan, 6 March 2011 While fumbling around with Mehler transforms, I think I spotted an obscure errata in your Differential Equations book, 3rd Edition 1997. I don't see it in your website 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 see: In something I wrote a while ago, I presented the transform in this manner: _______________________________________________________________________________ The generalized Mehler-Fock (Mehler-Fok) transform (Oberhettinger and Higgins* page 2) is this, g(y) = !Syntax Error, Idτ Pm-1/2+iτ(y) f(τ) // expansion f(τ) = (τ/π) sh(πτ) Γ(1/2-m+iτ) Γ(1/2-m-iτ)!Syntax Error, Idy Pm-1/2+iτ(y) g(y) // projection and for m = 0, using Γ(1/2+iτ)Γ(1/2-iτ) = π/cosh(πτ), one obtains the regular Mehler-Fock transform, g(y) = !Syntax Error, Idτ P-1/2+iτ(y) f(τ) // expansion f(τ) = τ th(πτ)!Syntax Error, Idy P-1/2+iτ(y) g(y) // projection which can also be written as G(ξ) = !Syntax Error, Idτ P-1/2+iτ(chξ) f(τ) // expansion f(τ) = τ th(πτ) !Syntax Error, Idξ shξ P-1/2+iτ(chξ) G(ξ) // projection * F. Oberhettinger and T. P. Higgins, Tables of Lebedev, Mehler and Generalized Mehler Transforms, (Boeing Scientific Research Laboratories, Mathematical No. 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 at the University of Wyoming. _______________________________________________________________________________ As another piece of evidence, here is a clip from your page 355 Nasim 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