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"Arial" ? ? ? 1 ? 0 1 "Times" 12 ? ? 5 0 c n 106 1 0 0 k 468 i"?n page ?p?a" ? 1 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 0 0 -1 -1 -1 -1 -1 0 1 1 0 2 0 ? ? ? ? ? ? ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" *|: ;bP8&c0!*Hypergeometric | |Series}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~V?f0 (Hypergeometric)~p0 1 ~V?f0 (P)~p0 1 ~V?f0 (f)~p0 1 ~V?v0 (I)~p0 1 ~V?v0 (t)~p0 1 ~V?v0 (k)~p0 1 ~V?v0 (j)~p0 1 ~V?v0 (z)~p0 1 ~V?v0 (y)~p0 1 ~V?v0 (x)~p0 1 ~V?c0 ('g)~p0 1 ~V?c0 ('b)~p0 1 ~V?c0 ('a)~p0 1 ~V?c0 (n)~p0 1 ~V?c0 (m)~p0 1 ~V?c0 (b)~p0 1 ~V?c0 (a)~p0 1 ~V?c3 ('N)~p0 1 ~V?c4 (i)~p0 1 ~V?c1 ('p)~p0 1 ~V?d16 (d)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})-# b'4`f#}" *|: ;bP8&c0!*Definition| |`f } ,HGradshteyn and Ryzhik 9,N100,I}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(Hypergeometric('a,'b,'g,z)=Summation(k):(0):(~ n)*(P('a,k)*P('b,k))/(P('g,k))*z^k/k!)~p1 1 ~A('a=?a)~p0 2 ~A('b=?b)~p0 255 ~A('g=?c)~p0 255 ~A(z=?z)~p0 255 ~A(Hypergeometric(?a,?b,?c,?z)=Summation(k):(0):(~ n)*(?z^k*P(?a,k)*P(?b,k))/(k!*P(?c,k)))~p0 2 ~d~sb/_!! } b00,! c#T"_c/__c/__! " # $"} ^ _~ ~A(P(t,m)=PiProduct(t+j):(j):(0):(m-1))~p1 1 ~A(P(?t,?m)=PiProduct(j+?t):(j):(0):(?m-1))~p0 2 ~d~sb/_!! } b00(! c#T"_c/__c/__! ""} ^ _~A(~ t=?t)~p0 255 ~A(m=?m)~p0 255 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[#! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4`f#}" *|: ;bP8&c0!*Application| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP8&c0!*Integrand| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(f(x)=(x-2)/(x^2-6*x+5)^(1/3))~p1 2 ~A(f(?x)=(?x-2)/(?x^2-6*?x+5)^(1/3))~p0 3 ~d~sb/_!!! } b00&!! c#T"_c/__c/__!"} ^ _~A(x=~ ?x)~p0 255 ~G1 1 163 372 0 1 5 4 10 (-2...9):(-5...5):(?=~ 0...2*'p):('p/5):(10)~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#@" *|: ;bP8&c0!*Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~R8405120 ? (x,y):(y=bottom...top):(x=left...right):(~ 0)~p0 1 ~gc1 2 ? 0 -2607 -4096 0 65535 -2607 4096 0 ~gc1 2 ? 0 -1117 -4096 0 65535 -1117 4096 0 ~gc1 2 ? 0 372 -4096 0 65535 372 4096 0 ~gc1 2 ? 0 1862 -4096 0 65535 1862 4096 0 ~gc1 2 ? 0 3351 -4096 0 65535 3351 4096 0 ~ ~R8405120 ? (x,y):(x=left...right):(y=bottom...~ top):(0)~p0 1 ~gc1 2 ? 0 -4096 -3277 0 65535 4096 -3277 0 ~gc1 2 ? 0 -4096 -1638 0 65535 4096 -1638 0 ~gc1 2 ? 0 -4096 0 0 65535 4096 0 0 ~gc1 2 ? 0 -4096 1638 0 65535 4096 1638 0 ~gc1 2 ? 0 -4096 3277 0 65535 4096 3277 0 ~ ~X2 8405120 (left,y):(y=bottom...top):(y)~p0 1 ~gc1 2 ? 0 -4096 -4096 0 65535 -4096 4096 0 ~X1 8405120 (~ x,bottom):(x=left...right):(x)~p0 1 ~gc1 2 ? 0 -4096 -4096 0 65535 4096 -4096 0 ~V?c64 (~ left)~p0 1 ~V?c65 (right)~p0 1 ~V?c66 (bottom)~p0 1 ~V?c67 (top)~p0 1 ~L2 255 ? 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