{VERSION 2 3 "DEC ALPHA UNIX" "2.3" } {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\"\"\"-%$sinG6#*&F$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(F+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(\"\"$F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expand(binomial(n+2,k -1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*0,&%\"nG\"\"\"\"\"#F&F&,(F%F &\"\"$F&%\"kG!\"\"F+,&F%F&F&F&F&,(F%F&F'F&F*F+F+F*F&,(F%F&F*F+F&F&F+-% )binomialG6$F%F*F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simpl ify(GAMMA(n+4)/n!);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"nG\"\"\" F&F&F&,&F%F&\"\"#F&F&,&F%F&\"\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int(t^(z-1)*exp(-t),t=0..infinity);" }}{PARA 6 "" 1 " " {TEXT -1 157 "Definite integration: Can't determine if the integral \+ is convergent.\nNeed to know the sign of --> z\nWill now try indefinit e integration and then take limits." }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%$intG6$*&)%\"tG,&%\"zG\"\"\"!\"\"F+F+-%$expG6#,$F(F,F+/F(;\"\"!%)in finityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(z,positiv e);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int(t^(z-1)*exp(-t), t=0..infinity);" }}{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 -1 160 "Definite integration: Can't determine if the integral is convergent.\nNeed to know the sign of -- > -w+1\nWill now 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$%#z|irG%#w|irG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "int(sin(phi)^(2*z-1)*cos(phi)^(2*w-1),phi=0..Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&)-%$sinG6#%$phiG,&%#z|irG \"\"#!\"\"\"\"\"F0)-%$cosGF*,&%#w|irGF.F/F0F0/F+;\"\"!,$%#PiG#F0F." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 }