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 | | http://functions.wolfram.com/01.18.16.0202.01 | 
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 | | a ArcSec[x] + b ArcCosh[y] == 
 (Pi a)/2 - 2 I Pi (Floor[(-Arg[(Sqrt[1 - 1/x^2] + I/x)^(I a)] - 
       Arg[(y + Sqrt[y - 1] Sqrt[y + 1])^b] + Pi)/(2 Pi)] + 
    Floor[(Pi - Im[b Log[y + Sqrt[y - 1] Sqrt[y + 1]]])/(2 Pi)] + 
    Floor[(Pi - Re[a Log[Sqrt[1 - 1/x^2] + I/x]])/(2 Pi)]) + 
  Log[(Sqrt[1 - 1/x^2] + I/x)^(I a) (y + Sqrt[y - 1] Sqrt[y + 1])^b] | 
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 | | Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List["ArcSec", "[", "x", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["ArcCosh", "[", "y", "]"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "a"]], "2"], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], "]"]]]], "-", 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["\[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["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Re", "[", RowBox[List["a", " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"]]], "]"]]]]]]]]]] | 
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   <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> ⁢ </mo>  <mrow>  <msup>  <mi> sec </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> ⁢ </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>  </mo>  <mrow>  <mfrac>  <mrow>  <mi> π </mi>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mn> 2 </mn>  </mfrac>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> π </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mrow>  <mo> - </mo>  <mrow>  <mi> arg </mi>  <mo> ⁡ </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> ⁢ </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>  </mrow>  <mo> - </mo>  <mrow>  <mi> arg </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <msup>  <mi> x </mi>  <mn> 2 </mn>  </msup>  </mfrac>  </mrow>  </msqrt>  <mo> + </mo>  <mfrac>  <mi> ⅈ </mi>  <mi> x </mi>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  </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>  <mi> Im </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> y </mi>  <mo> + </mo>  <mrow>  <msqrt>  <mrow>  <mi> y </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msqrt>  <mo> ⁢ </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> ⁢ </mo>  <mi> π </mi>  </mrow>  </mfrac>  <mo> ⌋ </mo>  </mrow>  <mo> + </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mi> π </mi>  <mo> - </mo>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <msup>  <mi> x </mi>  <mn> 2 </mn>  </msup>  </mfrac>  </mrow>  </msqrt>  <mo> + </mo>  <mfrac>  <mi> ⅈ </mi>  <mi> x </mi>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> π </mi>  </mrow>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <msup>  <mi> x </mi>  <mn> 2 </mn>  </msup>  </mfrac>  </mrow>  </msqrt>  <mo> + </mo>  <mfrac>  <mi> ⅈ </mi>  <mi> x </mi>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  </msup>  <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> ⁢ </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>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <plus />  <apply>  <times />  <ci> a </ci>  <apply>  <arcsec />  <ci> x </ci>  </apply>  </apply>  <apply>  <times />  <ci> b </ci>  <apply>  <arccosh />  <ci> y </ci>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <pi />  <ci> a </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </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>  <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>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <arg />  <apply>  <power />  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <times />  <imaginaryi />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <imaginaryi />  <ci> a </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>  <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>  <floor />  <apply>  <times />  <apply>  <plus />  <pi />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <real />  <apply>  <times />  <ci> a </ci>  <apply>  <ln />  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <times />  <imaginaryi />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> -1 </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>  <ln />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <times />  <imaginaryi />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <imaginaryi />  <ci> a </ci>  </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>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["ArcSec", "[", "x_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["ArcCosh", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "a"]], "2"], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], "]"]]]], "-", 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["\[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["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Re", "[", RowBox[List["a", " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"]]], "]"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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