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http://functions.wolfram.com/01.16.16.0191.01
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a ArcCot[x] + b ArcCot[y] ==
a Pi Floor[(-Arg[1 - I/x] + Arg[1 + I/x] + Pi)/(2 Pi)] -
2 I Pi (Floor[(-Arg[((1 - I/x)/(1 + I/x))^((I a)/2)] -
Arg[(1 - I/y)^((I b)/2)] + Pi)/(2 Pi)] +
Floor[(Pi - (1/2) Re[a Log[(1 - I/x)/(1 + I/x)]])/(2 Pi)] +
Floor[(Pi - (1/2) Re[b Log[1 - I/y]])/(2 Pi)]) -
2 I Pi (Floor[(-Arg[((1 - I/x)/(1 + I/x))^((I a)/2) (1 - I/y)^((I b)/2)] -
Arg[(1 + I/y)^((-(1/2)) (I b))] + Pi)/(2 Pi)] +
Floor[(Pi - Im[Log[((1 - I/x)/(1 + I/x))^((I a)/2) (1 - I/y)^((I b)/2)]])/
(2 Pi)] + Floor[((1/2) Re[b Log[1 + I/y]] + Pi)/(2 Pi)]) +
Log[(((1 - I/x)/(1 + I/x))^((I a)/2) (1 - I/y)^((I b)/2))/
(1 + I/y)^((1/2) (I b))]
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<mfrac> <mrow> <mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <mi> x </mi> </mfrac> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mi> x </mi> </mfrac> </mrow> </mfrac> <mo> ) </mo> </mrow> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mn> 2 </mn> </mfrac> </msup> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <mi> y </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mn> 2 </mn> </mfrac> </msup> <mo> ) </mo> </mrow> <mo> + </mo> <mi> π </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> <mo> + </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> π </mi> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> 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Date Added to functions.wolfram.com (modification date)
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