| |  
 |  | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | http://functions.wolfram.com/01.11.27.0064.01 | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | ArcSec[Sec[z]] == Piecewise[
  {{(-1)^Floor[Re[z]/Pi] (-z + Pi Floor[Re[z]/Pi] - Pi/2) + Pi/2, 
    Element[Re[z]/Pi, Integers] && Im[z] <= 0}, 
   {(-1)^Floor[Re[z]/Pi] (z - Pi Floor[Re[z]/Pi] - Pi/2) + Pi/2, True}}] | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Cell[BoxData[RowBox[List[RowBox[List["ArcSec", "[", RowBox[List["Sec", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["Piecewise", "[", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "z"]], "+", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]]], "-", FractionBox["Pi", "2"]]], ")"]]]], "+", FractionBox["\[Pi]", "2"]]], ",", RowBox[List[RowBox[List[FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]]], "-", FractionBox["Pi", "2"]]], ")"]]]], "+", FractionBox["\[Pi]", "2"]]], ",", "True"]], "}"]]]], "}"]], "]"]]]]]] | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 | | 
   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <msup>  <mi> sec </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <mrow>  <mi> sec </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ) </mo>  </mrow>  <mo>  </mo>  <mrow>  <mo>  </mo>  <mtable>  <mtr>  <mtd>  <mrow>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mi> π </mi>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mi> π </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mi> π </mi>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </mrow>  <mo> - </mo>  <mfrac>  <mi> π </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mfrac>  <mi> π </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  </mtd>  <mtd>  <mrow>  <mrow>  <mfrac>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mi> π </mi>  </mfrac>  <mo> ∈ </mo>  <semantics>  <mi> ℤ </mi>  <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation>  </semantics>  </mrow>  <mo> ∧ </mo>  <mrow>  <mrow>  <mi> Im </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ≤ </mo>  <mn> 0 </mn>  </mrow>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mi> π </mi>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mrow>  <mi> π </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ⌊ </mo>  <mfrac>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mi> π </mi>  </mfrac>  <mo> ⌋ </mo>  </mrow>  </mrow>  <mo> - </mo>  <mfrac>  <mi> π </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mfrac>  <mi> π </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  </mtd>  <mtd>  <mi> True </mi>  </mtd>  </mtr>  </mtable>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <arcsec />  <apply>  <sec />  <ci> z </ci>  </apply>  </apply>  <apply>  <ci> Piecewise </ci>  <list>  <list>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <cn type='integer'> -1 </cn>  <apply>  <floor />  <apply>  <times />  <apply>  <real />  <ci> z </ci>  </apply>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  <apply>  <times />  <pi />  <apply>  <floor />  <apply>  <times />  <apply>  <real />  <ci> z </ci>  </apply>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <pi />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <pi />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <and />  <apply>  <in />  <apply>  <times />  <apply>  <real />  <ci> z </ci>  </apply>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  <integers />  </apply>  <apply>  <leq />  <apply>  <imaginary />  <ci> z </ci>  </apply>  <cn type='integer'> 0 </cn>  </apply>  </apply>  </list>  <list>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <cn type='integer'> -1 </cn>  <apply>  <floor />  <apply>  <times />  <apply>  <real />  <ci> z </ci>  </apply>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <pi />  <apply>  <floor />  <apply>  <times />  <apply>  <real />  <ci> z </ci>  </apply>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <pi />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <pi />  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <true />  </list>  </list>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSec", "[", RowBox[List["Sec", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[Piecewise]", GridBox[List[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "z"]], "+", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]]], "-", FractionBox["\[Pi]", "2"]]], ")"]]]], "+", FractionBox["\[Pi]", "2"]]], RowBox[List[RowBox[List[FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]], List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]]], "-", FractionBox["\[Pi]", "2"]]], ")"]]]], "+", FractionBox["\[Pi]", "2"]]], "True"]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]]]]]] | 
 |  
 |   
 |  
 |  
 | |   
 |  
 |  
 |  
 |  
 |  
 |  
 | | Date Added to functions.wolfram.com (modification date) | 
 |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |   
 |  
 |  
 |  |  | 
 
 
 | 
 |