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Definition df-lgam 24803
 Description: Define the log-Gamma function. We can work with this form of the gamma function a bit easier than the equivalent expression for the gamma function itself, and moreover this function is not actually equal to because the branch cuts are placed differently (we do have , though). This definition is attributed to Euler, and unlike the usual integral definition is defined on the entire complex plane except the nonpositive integers , where the function has simple poles. (Contributed by Mario Carneiro, 12-Jul-2014.)
Assertion
Ref Expression
df-lgam
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-lgam
StepHypRef Expression
1 clgam 24800 . 2
2 vz . . 3
3 cc 8988 . . . 4
4 cz 10282 . . . . 5
5 cn 10000 . . . . 5
64, 5cdif 3317 . . . 4
73, 6cdif 3317 . . 3
82cv 1651 . . . . . . 7
9 vm . . . . . . . . . . 11
109cv 1651 . . . . . . . . . 10
11 c1 8991 . . . . . . . . . 10
12 caddc 8993 . . . . . . . . . 10
1310, 11, 12co 6081 . . . . . . . . 9
14 cdiv 9677 . . . . . . . . 9
1513, 10, 14co 6081 . . . . . . . 8
16 clog 20452 . . . . . . . 8
1715, 16cfv 5454 . . . . . . 7
18 cmul 8995 . . . . . . 7
198, 17, 18co 6081 . . . . . 6
208, 10, 14co 6081 . . . . . . . 8
2120, 11, 12co 6081 . . . . . . 7
2221, 16cfv 5454 . . . . . 6
23 cmin 9291 . . . . . 6
2419, 22, 23co 6081 . . . . 5
255, 24, 9csu 12479 . . . 4
268, 16cfv 5454 . . . 4
2725, 26, 23co 6081 . . 3
282, 7, 27cmpt 4266 . 2
291, 28wceq 1652 1
 Colors of variables: wff set class This definition is referenced by:  lgamgulm2  24820  lgamf  24826  iprodgam  25319
 Copyright terms: Public domain W3C validator