{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "M aple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "term:=GAMMA(z)*GAMMA(1-z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%termG*&-%&GAMMAG6#%\"zG\"\"\"-F'6#, &F*F*F)!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "simplify( term);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#PiG\"\"\"-%$sinG6#*&F$\" \"\"%\"zGF*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "convert (n!,GAMMA);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&GAMMAG6#,&%\"nG\"\" \"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "convert(binomial( n,k),factorial);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%*factorialG6#% \"nG\"\"\"*&-F%6#%\"kG\"\"\"-F%6#,&F'\"\"\"F,!\"\"\"\"\"!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expand(GAMMA(n+4));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*,-%&GAMMAG6#%\"nG\"\"\"F'F(,&F'F(F(F( F(,&F'F(\"\"#F(F(,&F'F(\"\"$F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expand(binomial(n+2,k-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&**,&%\"nG\"\"\"\"\"#F'F',&F&F'F'F'F'%\"kGF'-%)binomia lG6$F&F*F'\"\"\"*(,(F&F'\"\"$F'F*!\"\"\"\"\",(F&F'F(F'F*F2\"\"\",(F&F' F*F2F'F'\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simp lify(GAMMA(n+4)/n!);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"nG\"\" \"F&F&F&,&F%F&\"\"#F&F&,&F%F&\"\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int(t^(z-1)*exp(-t),t=0..infinity);" }}{PARA 6 "" 1 " " {TEXT -1 68 "Definite integration: Can't determine if the integral i s convergent." }}{PARA 6 "" 1 "" {TEXT -1 30 "Need to know the sign of --> z" }}{PARA 6 "" 1 "" {TEXT -1 57 "Will now try indefinite integra tion and then take limits." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6 $*&)%\"tG,&%\"zG\"\"\"!\"\"F+F+-%$expG6#,$F(F,F+/F(;\"\"!%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(z,positive);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int(t^(z-1)*exp(-t),t=0..inf inity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&GAMMAG6#%#z|irG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "int(t^(z-1)*(1-t)^(w-1),t=0. .1);" }}{PARA 6 "" 1 "" {TEXT -1 68 "Definite integration: Can't deter mine if the integral is convergent." }}{PARA 6 "" 1 "" {TEXT -1 33 "Ne ed to know the sign of --> -w+1" }}{PARA 6 "" 1 "" {TEXT -1 57 "Will n ow try indefinite integration and then take limits." }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%$intG6$*&)%\"tG,&%#z|irG\"\"\"!\"\"F+F+),&F+F+F(F,, &%\"wGF+F,F+F+/F(;\"\"!F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(w,positive);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " int(t^(z-1)*(1-t)^(w-1),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-% %BetaG6$%#w|irG%#z|irG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "i nt(sin(phi)^(2*z-1)*cos(phi)^(2*w-1),phi=0..Pi/2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&*&-%&GAMMAG6#%#w|irG\"\"\"-F'6#%#z|irGF*\"\"\"-F' 6#,&F)F*F-F*!\"\"#F*\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }