Robert Munafo has generously concatenated the four files.<http://www.tweedledum.com/rwg/Gosper%201990%20Strip%20Mining.pdf> On Mon, Jan 23, 2012 at 1:54 AM, Bill Gosper <billgosper@gmail.com> wrote:
The arboricidal version is
Gosper, R. Wm., Strip Mining in the Abandoned Orefields of Nineteenth Century Mathematics, Computers in Mathematics, (D. Chudnovsky & R. Jenks, eds.), Lecture Notes in Pure and Applied Mathematics, Vol 125 (1990), p282. but they printed my earliest draft instead of one of the many revisions I sent during the long publication delay. Better: http://www.tweedledum.com/rwg/stanfordn1.pdf http://www.tweedledum.com/rwg/stanfordn2.pdf http://www.tweedledum.com/rwg/stanfordn3.pdf http://www.tweedledum.com/rwg/stanfordn4.pdf (The machine I TeXed them on was too microcephalic to typeset more than a handful of pages per file! And it couldn't import graphics--there are some missing lines and a curve that were drawn by hand.) --rwg
JPropp>
Bill, what's the best reference to give people on path invariant matrix products?
I want to mention this to Alexei Borodin at MIT, since it seems relevant to some of the work he's done.
Jim Propp
Fooling with more path invariant matrices last nite, the kids & I found> HypergeometricPFQ[{1/2 - a, 1 - a, 1/2 + a, 1 + a,> 23/14 + (2 a)/7 - 1/7 Sqrt[1 - 3 a - 3 a^2],> 23/14 + (2 a)/7 + 1/7 Sqrt[1 - 3 a - 3 a^2]}, {5/4, 3/2, 7/4,> 9/14 + (2 a)/7 - 1/7 Sqrt[1 - 3 a - 3 a^2],> 9/14 + (2 a)/7 + 1/7 Sqrt[1 - 3 a - 3 a^2]}, -(1/48)] ==> (2 3^(3/2 + a) Sin[(a \[Pi])/3])/(a (11 + 12 a + 4 a^2))>> I don't recall any F[-1/48]. Julian found 27 a which rationalize the> parameters, e.g.,> HypergeometricPFQ[{46/43, 40/43, 49/86, 37/86, 883/602, 153/86}, {3/2,> 5/4, 7/4, 281/602, 67/86}, -1/48] ==> 159014*3^(37/86)*Sin[Pi/43]/18827>> There were three 3F2[-1/4]
Correction: 3F2[-1/48]
(which Macsyma could do), one 4F3,
HypergeometricPFQ[{-(3/4), -(1/4), 37/28, 9/4}, {1/4, 9/28, 3/2}, -(1/48)] == (8 (Sqrt[2] + Sqrt[6]))/(15 3^(3/4)) --rwg
and no 5F4s.>> Along the way, he found the minor simplification puzzle> 1 == 10*Sqrt[Pi]^3/(27*2^(2/3)*(1/3)!^2*(5/6)!*Sqrt[3])>> and the unlikely looking> 3*((4*Sqrt[3]*I + 1)/Sqrt[1 - I/4/Sqrt[3]] - (4*Sqrt[3]*I -> 1)/Sqrt[I/4/Sqrt[3] + 1]) -> 14*3^(1/4)*((47*Sqrt[3]*I + 24)/> Sqrt[4*Sqrt[3] - I]^5 - (47*Sqrt[3]*I - 24)/Sqrt[I + 4*Sqrt[3]]^5) ==> 121*Sqrt[Pi]^5/(288*2^(1/3)*(1/6)!*(1/4)!^2*(11/12)!^2*Sqrt[3])>> We also accelerated Dixon's thm to get a three-parameter 7F6[-1/4]:> HypergeometricPFQ[{a, b, c,> 2*a - 2*b, -c - b + 2*a, (r + 3*c - b + 4*a)/10 +> 1, (-r + 3*c - b + 4*a)/10 + 1}, {c - b + 1, (1 - b)/2 + a, -b/2 +> a + 1, c + b - a + 1, (-r + 3*c - b + 4*a)/> 10, (r + 3*c - b + 4*a)/10}, -1/> 4] == (2*a - b)!*2^(2*b - 2*a)*(c - b)!*(c + b - a)!*> Sqrt[Pi]/(a!*(-b + a - 1/2)!*c!*(c - a)!)>> r-> Sqrt[(3*c - b)^2 - 8*a*(2*c + b - 2*a)]>> a rational case of which is> HypergeometricPFQ[{3/2 + a/2, 2 + a/2, 1 - c, 1 + a + 2 c,> 1 + a/2 - c - (2 c)/a, 8/5 + a/5 - (2 c)/5 - (6 c)/(5 a),> 1 + a/2 + 2 c + (2 c)/a}, {1 + a/2, 3/2 + a/2 + c/2, 2 + a/2 + c/2,> 1 + a/2 - (2 c)/a, 3/2 - 2 c - (2 c)/a,> 3/5 + a/5 - (2 c)/5 - (6 c)/(5 a)}, -(1/4)] == (> 2^(-1 - a - 2 c)> Sqrt[\[Pi]] (2 + a + c)! (a/2 - (2 c)/a)! (1/2 - 2 c - (2 c)/> a)!)/(((3 + a)/> 2)! (a/2 + c)! (-(1/2) - c - (2 c)/a)! (1 + a/2 - c - (2 c)/a)!)> --rwg