a ArcTanh[x] + b ArcCosh[y] == I a Pi Floor[(-Arg[1 - x] + Arg[x + 1] + Pi)/(2 Pi)] - 2 I Pi (Floor[(-Arg[((1 - x)/(x + 1))^(-(a/2))] - Arg[(y + Sqrt[y - 1] Sqrt[y + 1])^b] + Pi)/(2 Pi)] + Floor[((1/2) Im[a Log[(1 - x)/(x + 1)]] + Pi)/(2 Pi)] + Floor[(Pi - Im[b Log[y + Sqrt[y - 1] Sqrt[y + 1]]])/(2 Pi)]) + I Pi (1 - (-1)^Floor[Arg[(y + Sqrt[y - 1] Sqrt[y + 1])^b/((1 - x)/(x + 1))^ (a/2) + 1]/(2 Pi) + 1/2]) + 2 ArcTanh[((y + Sqrt[y - 1] Sqrt[y + 1])^b/((1 - x)/(x + 1))^(a/2) - 1)/ ((y + Sqrt[y - 1] Sqrt[y + 1])^b/((1 - x)/(x + 1))^(a/2) + 1)]

Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List["ArcTanh", "[", "x", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["ArcCosh", "[", "y", "]"]]]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List["1", "-", "x"]], "]"]]]], "+", RowBox[List["Arg", "[", RowBox[List["x", "+", "1"]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], "]"]]]], "]"]]]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]]]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "+", FractionBox["1", "2"]]], "]"]]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"]]], "-", "1"]], RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]]]], "+", "1"]]], "]"]]]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cosh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> y </mi> <mo> + </mo> <mrow> <msqrt> <mrow> <mi> y </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> b </mi> </msup> <mo> ) </mo> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> <mo> + </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> <mo> + </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> - </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> y </mi> <mo> + </mo> <mrow> <msqrt> <mrow> <mi> y </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> &#8970; </mo> <mrow> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> y </mi> <mo> + </mo> <mrow> <msqrt> <mrow> <mi> y </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> b </mi> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8971; </mo> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> y </mi> <mo> + </mo> <mrow> <msqrt> <mrow> <mi> y </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> b </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> y </mi> <mo> + </mo> <mrow> <msqrt> <mrow> <mi> y </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> b </mi> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> x </mi> </mrow> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <arctanh /> <ci> x </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <arccosh /> <ci> y </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <imaginaryi /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <apply> <plus /> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <power /> <apply> <plus /> <ci> y </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <imaginary /> <apply> <times /> <ci> a </ci> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <ci> b </ci> <apply> <ln /> <apply> <plus /> <ci> y </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <pi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <plus /> <apply> <times /> <apply> <arg /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <arctanh /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["ArcTanh", "[", "x_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["ArcCosh", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List["1", "-", "x"]], "]"]]]], "+", RowBox[List["Arg", "[", RowBox[List["x", "+", "1"]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], "]"]]]], "]"]]]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]]]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "+", FractionBox["1", "2"]]], "]"]]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"]]], "-", "1"]], RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", "x"]], RowBox[List["x", "+", "1"]]], ")"]], RowBox[List["-", FractionBox["a", "2"]]]]]], "+", "1"]]], "]"]]]]]]]]]]

2007-05-02