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? 1 26177 26178 26115 26178 1 1 1 1 0 0
8405120 0 -1 0 1 -1 -1 -1 -1 -1 0
1 1 0 2 0 ? ? ? ? ? ? ? ? 
~Q
]|Expr|[#b @`bb#_b#_b#_})## b'4" *|: ;bP8&c0!*Gamma Function|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
1 ~V?f32 (log)~p0
2 ~V?f307 (ln)~p0
2 ~V?f291 (exp)~p0
2 ~V?c2 (e)~p0
2 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Standard Rules|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers|
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2 ~Ht(?x^(-?y)):(1/?x^?y)~p0
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3 ~Hs(e^(ln(?x))):(?x)~p0
3 ~Hs(10^(log(?x))):(?x)~p0
3 ~Hs(?y^(log_?y(?x))):(?x)~p0
3 ~Hs(ln(e^?x)):(?x)~p0
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3 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0
3 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0
3 ~He(log(sqrt(?u))):(1/2*log(?u))~p0
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]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Integration Rules|
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2 ~V?c1 ('p)~p0
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3 ~Q
]|Expr|[#b @`bb#_b#_b#_}))# b$8" *|: ;bP8&c0!*after Partial Fraction|
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3 ~Hs(ln(?x+?b*j)):((-j*arctan(?x/?b)+1/2*ln(?x^~
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4 ~Hs(ln(?x-?b*j)):((j*arctan(?x/?b)+1/2*ln(?x^2+~
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4 ~Hs(ln(?x-j)):((j*arctan(?x)+1/2*ln(?x^2+1))+1/~
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4 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$4" *|: ;bP8&c0!*Derivatives of |
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3 ~Ht(Diff(?x)*(Integral(?y*d*?x))):(?y)~p0
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(-5...5):(-4...4):(?=~
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]|Expr|[#b @`bb#_b#_b#_})!# b#@" *|: ;bP8&c0!*Declarations|
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~
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1 ~gc1 2 ? 0 -4096 -2048 0
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~gc1 2 ? 0 -4096 0 0
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~
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~X1 8405120 (~
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~t~p0
0 ~T~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})?# b#8" *|: ;bP8&c0!*Enter real|
  | and imaginary parts of z ,] a ,K ib to compute "!Symbol^:!&c0  G|
  |: &c0!*,Hz,I,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(a=2.1000000000000001)~p0
0 ~d~A(b=1)~p0
255 ~d~A(z=a+i*b)~p0
255 ~d~A('G(z))~p0
0 ~A('G(z)=0.67295245678381044+0.40338515498215272*~
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255 ~sb/^!!   }
$&!  c#T"!c#L"_c/__c/__}
^ _~t~p0
0 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4`f#}" *|: ;bP8&c0!*Definition|
  |}& 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('G(n)=Integral(e^(-x)*x^(n-1)*d*x):(0):('N))~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b'4" *|: ;bP8&c0!*n ,^ 0|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
255 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f#})## b'4" *|: ;bP8&c0!*Recursion|
  | Rules}& 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!*a,N|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A('G(1)=Integral(e^(-x)*x^(1-1)*d*x):(0):('N))~p0
2 ~sb/_!    }
b00&   c#T"_c/__c/__!"}
^ _~A(n=1)~p0
255 ~A('G(1)=Integral(e^(-x)*d*x):(0):('N))~p0
3 ~sb/_!    }
!(   c#T"!c&H# c"H$_ "}
^ _~A('G(1)=~
 1.0000000017273587)~p0
255 ~sb/_!    }
$&   c#T"!c&H#_c/__c/__}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})"# b'4" *|: ;bP8&c0!*b,N|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A('G(n+1)=Integral(e^(-x)*x^((n+1)-1)*d*x):(0):(~
 'N))~p0
2 ~sb/_!    }
b00&   c#T"_c/__c/__!"}
^ _~A(n=n+~
 1)~p0
255 ~A('G(n+1)=EvaluateAt(Integral(e^(-x)*x^n*d*x)):(~
 x=0):(x='N))~p0
3 ~sb/_!!   }
!&!  c#T"!c&H#_c/__c/__}
^ _~A('G(~
 n+1)=EvaluateAt(Integral(x^n*e^(-x)*d*x)):(x=0):(~
 x='N))~p0
4 ~sb/_!!   }
b0++!  c#T"!c"D# c&H! c"H$_ !"}
^ _~
 ~A(u=x^n)~p0
255 ~A(d*v=e^(-x)*d*x)~p0
255 ~A('G(n+1)=EvaluateAt(-e^(-x)*x^n+n*(Integral(~
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5 ~sb/_!!   }
/+!  c#T"!c"D# c&H! c"H$_!$[}
^ _~A(~
 'G(n+1)=0^n+(EvaluateAt(n*(Integral(e^(-x)*x^(~
 n-1)*d*x))):(x=0):(x='N)))~p0
6 ~sb/_!!   }
!&!  c#T"!c"D#_c/__c/__}
^ _~A('G(~
 n+1)=n*(Integral(e^(-x)*x^(n-1)*d*x):(0):('N)))~p0
7 ~A('G(n+1)=n*'G(n))~p0
8 ~sb/_!!   }
b00*!  c#T"!c"H"!c&H#_c/__c/__!#}
^ _~
 ~Q
]|Expr|[#b @`bb#_b#_b#_})"# b'4" *|: ;bP8&c0!*c,N|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A('G(n+1)=n*'G(n))~p0
2 ~A('G(n+1)=n*(n-1)*'G(n-1))~p0
3 ~A('G(n+1)=n*(n-1)*(n-2)...(n-(floor(n)-1))*'G(~
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4 ~A('G(n+1)=n!)~p0
5 ~Q
]|Expr|[#b @`bb#_b#_b#_})+# b'4" *|: ;bP8&c0!*if n is a positive|
  | integer}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
255 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4[&! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f#})-# b'4" *|: ;bP8&c0!*Sample|
  | Calculation for n ,] 20,N3}& 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'4Sterling,Gs Approximation|
  | for Large Positive n}& b!( b"0 b#8 b$@ b%H b&P!WW})+# b'4,HGradshteyn|
  | and Ryzhik 8,N327,I}& b!( b"0 b#8 b$@ b%H b&P!WW}) # 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 ~A('G_1(n)=n^n*e^(-n)*sqrt((2*'p)/n)*(1+1/(12*~
 n)+1/(288*n^2)-139/(51840*n^3)-571/(2488320*n^~
 4)))~p0
1 ~A('G_1(20.300000000000001)=3.4990668798205338e26*~
 1/e^20.300000000000001*sqrt(0.09852216748768472*~
 'p))~p0
2 ~sb/_!!   }
b00&!  c#T"_c/__c/__!"}
^ _~A(n=20.300000000000001)~p0
255 ~A('G_1(20.300000000000001)=2.9724610745605882e17)~p0
3 ~sb/_!!   }
$&!  c#T"!c"H"_c/__c/__}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP8&c0!*Check|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A('G(20.300000000000001))~p0
255 ~A('G(20.300000000000001)=2.972461809965289e17)~p0
255 ~sb/^!!   }
$&!  c#T"!c#L"_c/__c/__}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4[#! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f#})-# b'4" *|: ;bP8&c0!*Sample|
  | Calculations for n ,] 2,N1}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A('G_2(n)=Integral(e^(-x)*x^(n-1)*d*x):(0):('N))~p0
1 ~A(n=2.1000000000000001)~p0
255 ~A('G_2(2.1000000000000001)=Integral(e^(-x)*x^~
 (2.1000000000000001-1)*d*x):(0):('N))~p0
2 ~sb/_!    }
b00&   c#T"_c/__c/__!"}
^ _~A('G_2(~
 2.1000000000000001)=Integral(e^(-x)*x^1.1000000000000001*~
 d*x):(0):('N))~p0
3 ~sb/_!    }
!,   c#T"!c&H# c"H$!c%X"!c"L"_c/__c/__}
^ _~
 ~A(y=e^(-x)*x^1.1000000000000001)~p0
1 ~d~G1 1 160 352
0 1 5 4 10
(0...10):(0...0.40000000000000002):(~
 ?=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 ~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~
 ~R8405120 ? (x,y):(x=left...right):(y=bottom...~
 top):(0)~p0
1 ~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~gc-1 30 ? 0 -32768 -32768 -32768
2541 -32768 -32768 -32768
4519 -32768 -32768 -32768
6779 -32768 -32768 -32768
8757 -32768 -32768 -32768
11299 -32768 -32768 -32768
13558 -32768 -32768 -32768
16100 -32768 -32768 -32768
18078 -32768 -32768 -32768
20338 -32768 -32768 -32768
22316 -32768 -32768 -32768
24858 -32768 -32768 -32768
27117 -32768 -32768 -32768
29659 -32768 -32768 -32768
31637 -32768 -32768 -32768
33897 -32768 -32768 -32768
35875 -32768 -32768 -32768
38417 -32768 -32768 -32768
40676 -32768 -32768 -32768
43218 -32768 -32768 -32768
45196 -32768 -32768 -32768
47456 -32768 -32768 -32768
49434 -32768 -32768 -32768
51976 -32768 -32768 -32768
54235 -32768 -32768 -32768
56777 -32768 -32768 -32768
58755 -32768 -32768 -32768
61015 -32768 -32768 -32768
62993 -32768 -32768 -32768
65535 -32768 -32768 -32768
~
 ~X2 8405120 (left,y):(y=bottom...top):(y)~p0
1 ~gc-1 2 ? 0 -32768 -32768 -32768
65535 -32768 -32768 -32768
~
 ~X1 8405120 (x,bottom):(x=left...right):(x)~p0
1 ~gc-1 2 ? 0 -32768 -32768 -32768
65535 -32768 -32768 -32768
~
 ~V?c64 (left)~p0
1 ~V?c65 (right)~p0
1 ~V?c66 (bottom)~p0
1 ~V?c67 (top)~p0
1 ~L1 0 ? (x,y):(x=left...right)~p0
0 ~gc-1 82 ? 0 -32768 -32768 -32768
910 -32768 -32768 -32768
1618 -32768 -32768 -32768
2427 -32768 -32768 -32768
3135 -32768 -32768 -32768
4045 -32768 -32768 -32768
4854 -32768 -32768 -32768
5764 -32768 -32768 -32768
6472 -32768 -32768 -32768
7281 -32768 -32768 -32768
7989 -32768 -32768 -32768
8899 -32768 -32768 -32768
9708 -32768 -32768 -32768
10618 -32768 -32768 -32768
11327 -32768 -32768 -32768
12136 -32768 -32768 -32768
12844 -32768 -32768 -32768
13754 -32768 -32768 -32768
14563 -32768 -32768 -32768
15473 -32768 -32768 -32768
16181 -32768 -32768 -32768
16990 -32768 -32768 -32768
17698 -32768 -32768 -32768
18608 -32768 -32768 -32768
19417 -32768 -32768 -32768
20327 -32768 -32768 -32768
21035 -32768 -32768 -32768
21845 -32768 -32768 -32768
22553 -32768 -32768 -32768
23463 -32768 -32768 -32768
24272 -32768 -32768 -32768
25182 -32768 -32768 -32768
25890 -32768 -32768 -32768
26699 -32768 -32768 -32768
27407 -32768 -32768 -32768
28317 -32768 -32768 -32768
29126 -32768 -32768 -32768
30036 -32768 -32768 -32768
30744 -32768 -32768 -32768
31553 -32768 -32768 -32768
32261 -32768 -32768 -32768
33172 -32768 -32768 -32768
33981 -32768 -32768 -32768
34891 -32768 -32768 -32768
35599 -32768 -32768 -32768
36408 -32768 -32768 -32768
37116 -32768 -32768 -32768
38026 -32768 -32768 -32768
38835 -32768 -32768 -32768
39745 -32768 -32768 -32768
40453 -32768 -32768 -32768
41262 -32768 -32768 -32768
41970 -32768 -32768 -32768
42880 -32768 -32768 -32768
43690 -32768 -32768 -32768
44600 -32768 -32768 -32768
45308 -32768 -32768 -32768
46117 -32768 -32768 -32768
46825 -32768 -32768 -32768
47735 -32768 -32768 -32768
48544 -32768 -32768 -32768
49454 -32768 -32768 -32768
50162 -32768 -32768 -32768
50971 -32768 -32768 -32768
51679 -32768 -32768 -32768
52589 -32768 -32768 -32768
53398 -32768 -32768 -32768
54308 -32768 -32768 -32768
55017 -32768 -32768 -32768
55826 -32768 -32768 -32768
56534 -32768 -32768 -32768
57444 -32768 -32768 -32768
58253 -32768 -32768 -32768
59163 -32768 -32768 -32768
59871 -32768 -32768 -32768
60680 -32768 -32768 -32768
61388 -32768 -32768 -32768
62298 -32768 -32768 -32768
63107 -32768 -32768 -32768
64017 -32768 -32768 -32768
64624 -32768 -32768 -32768
65535 -32768 -32768 -32768
~t~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f#}))# b'4" *|: ;bP8&c0!*Simpson|
  |,Gs one,Mthird rule}& b!( b"0 b#8 b$@ b%H b&P!WW}}|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b$@" *|: ;bP8&c0!*input|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
2 ~A(f(x)=e^(-x)*x^1.1000000000000001)~p1
3 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"0" *|: ;bP8&c0!*integrand|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
255 ~A(f(?x)=e^(-?x)*?x^1.1000000000000001)~p0
4 ~d~sb/_!!   }
b00&!  c#T"_c/__c/__!"}
^ _~A(x=~
 ?x)~p0
255 ~A(a=0)~p0
3 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})## b"0" *|: ;bP8&c0!*lower bound|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
255 ~A(b=20)~p0
3 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})## b"0" *|: ;bP8&c0!*upper bound|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
255 ~A(k=200)~p1
3 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})'# b#8" *|: ;bP8&c0!*even number of |
  |panels}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
255 ~A('Dx=(b-a)/k)~p0
4 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})## b$@" *|: ;bP8&c0!*approximate <c" #|
  |(&f,Hx,I dx}^a^b}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
2 ~A('G_2(2.1000000000000001)='Dx/3*(f(a)+f(b)+2*~
 (Summation(j):(1):(k-1)*(mod(j,2)+1)*f(a+j*'Dx))))~p0
3 ~A('G_2(2.1000000000000001)=1.0465394175325471)~p0
4 ~sb/_!!   }
$&!  c#T"!c"H"_c/__c/__}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4[#! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})/# b'4`f#}" *|: ;bP8&c0!*Product|
  | representation`f } ,HGradshteyn and Ryzhik 8,N322,I|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}}|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A(n=2.1000000000000001)~p0
2 ~A(m=40000)~p0
255 ~A('G_3(n)=1/n*(PiProduct((1+1/j)^n/(1+n/j)):(~
 j):(1):(m)))~p1
2 ~A('G_3(2.1000000000000001)=1.0464556311691524)~p0
255 ~sb/_!    }
$&   c#T"!c"H"_c/__c/__}
^ _~A('G_~
 3(2.1000000000000001)=1/2.1000000000000001*(PiProduct(~
 (1+1/j)^2.1000000000000001/(1+2.1000000000000001/~
 j)):(j):(1):(40000)))~p0
3 ~sb/_!    }
b00(   c#T"_c/__c/__! ""}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})!# b'4`f }["! `f#}) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})+# b'4" *|: ;bP8&c0!*Sample Calculation|
  | for n ,] 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 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4[#! ) # b'4|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})## b'4`f#}" *|: ;bP8&c0!*Series|
  | representation}& b!( b"0 b#8 b$@ 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
1 ~A(n=i)~p0
2 ~A(m=40000)~p0
255 ~A('G_4(n)=1/n*exp(Summation(j):(1):(m)*ln((1/~
 j+1)^n/(1+n/j))))~p1
2 ~A('G_4(i)=-0.15494554005836575-0.49802383007697237*~
 i)~p0
255 ~sb/_!!   }
$&!  c#T"!c"T!_c/__c/__}
^ _~A('G_~
 4(i)=-i*e^(Summation(j):(1):(40000)*ln((1/j+1)^~
 i/(i/j+1))))~p0
3 ~sb/_!!   }
b00(!  c#T"_c/__c/__! ""}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP8&c0!*Check|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
2 ~A('G(n))~p0
255 ~A('G(n)='G(i))~p0
255 ~sb/^!!   }
b00*!  c#T"!c#L"!c'8 _c/__c/__!"}
^ _~
 ~A('G(n)=-0.15494978678875718-0.49801562685863177*~
 i)~p0
3 ~sb/_!!   }
$&!  c#T"!c#L"_c/__c/__}
^ _~c7
5 60 -1 4 60 -1 1 60 -1 53 -1 2 60 -1 52 -1 3 60 -1 54 -1 ~c2
66 -1 62 -1 67 -1 ~c1
68 -1 66 -1 ~c1
69 -1 68 -1 ~c2
71 -1 62 -1 72 -1 ~c1
73 -1 71 -1 ~c1
74 -1 73 -1 ~c1
77 -1 74 -1 ~c1
78 -1 77 -1 ~c2
80 -1 79 -1 62 -1 ~c2
89 -1 88 -1 90 -1 ~c1
91 -1 89 -1 ~c1
94 -1 93 -1 ~c2
98 -1 96 -1 97 -1 ~c1
99 -1 98 -1 ~c2
106 -1 104 -1 107 -1 ~c11
117 -1 116 -1 108 -1 53 -1 106 -1 44 -1 110 -1 52 -1 112 -1 48 -1 114 -1 43 -1 ~c1
122 -1 123 -1 ~c3
123 -1 121 -1 120 -1 119 -1 ~c1
129 -1 130 -1 ~c3
130 -1 128 -1 126 -1 127 -1 ~c2
133 -1 132 -1 126 -1 ~c1
134 -1 133 -1 ~e