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"6%%2elementary_chargeG/%'symbolG%\"eG/%'deriveG*&\"\"##\" \"\"F***%&alphaGF,%\"hGF,&%#muG6#\"\"!!\"\"%\"cGF4F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%9speed_of_light_in_vacuumG/%'symbolG%\"cG/%&valueG \"*eCz*H/%,uncertaintyG\"\"!/%&unitsG*&%\"mG\"\"\"%\"sG!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "evalf(eval(c, c=Constant(c)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*eCz*H\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "lambda[max] := evalf(eval(lambda[max], \{ c=Constant(c), h=Constant(h), k=Constant(k)\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'lambdaG6#%$maxG,$*&$\"+n'ox*G!#7\"\"\"%\"TG!\"\"F- " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "lambda[max] := 'lambda[ max]';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'lambdaG6#%$maxGF$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Rad := int(In(lambda,T), lam bda=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$RadG,$*&#\"\" \"\"#:F(*(,&*&#F)\"\"#F(*&%#PiGF(-%&limitG6%*&,,*&)%\"cG\"\"%F()%\"hGF 9F(!\"\"*0F9F()F8\"\"$F(%\"kGF(%\"TGF(-%#lnG6#,&-%$expG6#*,F;F(F8F(%'l ambdaGF " 0 "" {MPLTEXT 1 0 4 "Rad;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"#:F&*(,&*&#F'\"\"#F&*&%#PiGF&-%&limitG6%*&,,*&)%\"c G\"\"%F&)%\"hGF7F&!\"\"*0F7F&)F6\"\"$F&%\"kGF&%\"TGF&-%#lnG6#,&-%$expG 6#*,F9F&F6F&%'lambdaGF:F>F:F?F:F:F&F&F&FHF&)F9F=F&F&*0\"#7F&)F>F,F&)F? F,F&-%(polylogG6$F,FDF&)FHF,F&)F9F,F&)F6F,F&F&*0\"#CF&)F>F=F&)F?F=F&-F O6$F=FDF&)FHF=F&F9F&F6F&F:*,FUF&)F>F7F&)F?F7F&-FO6$F7FDF&)FHF7F&F&F&FH !\"%/FH\"\"!%&rightGF&F&F:**F,F&)F.\"\"&F&FfnF&FgnF&F&F&F6!\"#F9!\"$F& F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "evalf(eval(Rad, \{c=C onstant(c), h=Constant(h), k=Constant(k)\}));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,&*&$\"+cMt2g\"#t\"\"\"-%&limitG6%*&,,*&)-%)ConstantG6# %\"cG\"\"%F()-F16#%\"hGF4F(!\"\"*0F4F()F0\"\"$F(-F16#%\"kGF(%\"TGF(-%# lnG6#,&-%$expG6#*,F6F(F0F(%'lambdaGF9F=F9F@F9F9F(F(F(FIF()F6F " 0 "" {MPLTEXT 1 0 25 "evalf(eval(Constant(c)));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*eCz*H\"\"!" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 66 "int(In(lambda,T), lambda=0..infinity) assuming h>0, c>0, k>0, T>0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"# :F&*(,&*&#F'\"\"#F&*&%#PiGF&-%&limitG6%*&,,*&)%\"cG\"\"%F&)%\"hGF7F&! \"\"*0F7F&)F6\"\"$F&%\"kGF&%\"TGF&-%#lnG6#,&-%$expG6#*,F9F&F6F&%'lambd aGF:F>F:F?F:F:F&F&F&FHF&)F9F=F&F&*0\"#7F&)F>F,F&)F?F,F&-%(polylogG6$F, FDF&)FHF,F&)F9F,F&)F6F,F&F&*0\"#CF&)F>F=F&)F?F=F&-FO6$F=FDF&)FHF=F&F9F &F6F&F:*,FUF&)F>F7F&)F?F7F&-FO6$F7FDF&)FHF7F&F&F&FH!\"%/FH\"\"!%&right GF&F&F:**F,F&)F.\"\"&F&FfnF&FgnF&F&F&F6!\"#F9!\"$F&F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "assume(h>0, c>0, k>0, T>0);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Rad := int(In(lambda,T), lam bda=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$RadG,$*0\"\"# \"\"\"\"#:!\"\"%#PiG\"\"&%#c|irG!\"#%#h|irG!\"$%#k|irG\"\"%%#T|irGF2F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "evalf(eval(Rad, \{c=Con stant(c), h=Constant(h), k=Constant(k)\}));" }}{PARA 8 "" 1 "" {TEXT -1 68 "Error, (in ScientificConstants:-Constant) Constant `c` is not k nown\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "lprint(Rad);" }} {PARA 6 "" 1 "" {TEXT -1 25 "2/15*Pi^5/c^2/h^3*k^4*T^4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "Rad2 := evalf(eval(lprint(Rad), \{c =Constant(c), h=Constant(h), k=Constant(k)\}));" }}{PARA 6 "" 1 "" {TEXT -1 25 "2/15*Pi^5/c^2/h^3*k^4*T^4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Rad2G6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "about(c );" }}{PARA 6 "" 1 "" {TEXT -1 25 "Originally c, renamed c~:" }}{PARA 6 "" 1 "" {TEXT -1 47 " is assumed to be: RealRange(Open(0),infinity) " }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "unassign('h', 'c', 'k', 'T');" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "Rad;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*0\" \"#\"\"\"\"#:!\"\"%#PiG\"\"&%#c|irG!\"#%#h|irG!\"$%#k|irG\"\"%%#T|irGF 0F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "evalf(eval(2*Pi^5*k^ 4*T^4/(15*c^2*h^3), \{c=Constant(c), h=Constant(h), k=Constant(k)\})); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&$\"+o*)Rqc!#<\"\"\")%\"TG\"\"% F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "34 0 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }