html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 EllipticE

 http://functions.wolfram.com/08.04.06.0072.01

 Input Form

 EllipticE[z, m] == (-1)^Round[Re[z]/Pi] (Sqrt[(-m) Sin[z]^2]/(4 m Sin[z])) (2 m Sin[z]^2 Sqrt[1 - Csc[z]^2/m] - 2 Log[1 + Sqrt[1 - Csc[z]^2/m]] + (3/(8 m^2 Sin[z]^2)) Sum[((Pochhammer[3/2, k] Pochhammer[5/2, k])/ (m^k (k + 1)!)) HypergeometricPFQRegularized[{1, 1, 5/2 + k}, {4 + k, 2}, Csc[z]^2/m], {k, 0, Infinity}] + (1/Pi) (Pi (1 + 3 m + m Cos[2 z] + Log[4]) + 4 (-1 + m) (2 + Log[-4 m Sin[z]^2]) EllipticK[1/m] - 4 m EllipticE[1/m] (4 + Log[-4 m Sin[z]^2])) + (1/(8 m)) HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 3}, 1/m] + (9/(8 m^2)) Sum[(Pochhammer[5/2, k]^2/(m^k ((2 + k)! (3 + k)!))) Sum[1/(j + k + 3), {j, 0, k}], {k, 0, Infinity}] + 2 m Sin[z]^2 Sum[((Pochhammer[1/2, k] Pochhammer[-(1/2), k])/(m^k k!^2)) HypergeometricPFQ[{1, 1, 1/2 + k}, {2, 1 + k}, Sin[z]^2], {k, 0, Infinity}]) + 2 Round[Re[z]/Pi] EllipticE[m]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "m"]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]], RowBox[List["4", " ", "m", " ", RowBox[List["Sin", "[", "z", "]"]]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"], "m"]]]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"], "m"]]]]]], "]"]]]], "+", " ", RowBox[List[FractionBox["3", RowBox[List["8", " ", SuperscriptBox["m", "2"], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "2"], ",", "k"]], "]"]], SuperscriptBox["m", RowBox[List["-", "k"]]]]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "!"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List[FractionBox["5", "2"], "+", "k"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["4", "+", "k"]], ",", "2"]], "}"]], ",", FractionBox[SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"], "m"]]], "]"]]]]]]]], "+", " ", RowBox[List[FractionBox["1", "\[Pi]"], RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["3", " ", "m"]], "+", RowBox[List["m", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["Log", "[", "4", "]"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], RowBox[List["(", RowBox[List["2", "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox["1", "m"], "]"]]]], " ", "-", RowBox[List["4", " ", "m", " ", RowBox[List["EllipticE", "[", FractionBox["1", "m"], "]"]], " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["8", " ", "m"]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", "3"]], "}"]], ",", FractionBox["1", "m"]]], "]"]]]], "+", RowBox[List[FractionBox["9", RowBox[List["8", SuperscriptBox["m", "2"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "2"], ",", "k"]], "]"]], "2"], SuperscriptBox["m", RowBox[List["-", "k"]]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "+", "k"]], ")"]], "!"]], RowBox[List[RowBox[List["(", RowBox[List["3", "+", "k"]], ")"]], "!"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "k"], FractionBox["1", RowBox[List["j", "+", "k", "+", "3"]]]]]]]]]]], "+", RowBox[List["2", " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["m", RowBox[List["-", "k"]]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "k"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "2"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List[FractionBox["1", "2"], "+", "k"]]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", RowBox[List["1", "+", "k"]]]], "}"]], ",", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]]]]]]]], " ", ")"]]]], "+", RowBox[List["2", " ", RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["EllipticE", "[", "m", "]"]]]]]]]]]]]]

 MathML Form

 E ( z m ) 2 Re ( z ) π E ( m ) + ( - 1 ) Re ( z ) π - m sin 2 ( z ) 4 m sin ( z ) ( 2 1 - csc 2 ( z ) m m sin 2 ( z ) + 2 m sin 2 ( z ) k = 0 m - k ( 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "k"], Pochhammer] ( - 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "2"]]], ")"]], "k"], Pochhammer] ( k ! ) 2 3 F 2 ( 1 , 1 , k + 1 2 ; 2 , k + 1 ; sin 2 ( z ) ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[SuperscriptBox["sin", "2"], "(", "z", ")"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + 1 8 m 4 F 3 ( 1 , 1 , 3 2 , 3 2 ; 2 , 2 , 3 ; 1 m ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["1", "m"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 2 log ( 1 - csc 2 ( z ) m + 1 ) + 1 π ( π ( cos ( 2 z ) m + 3 m + log ( 4 ) + 1 ) + 4 ( m - 1 ) K ( 1 m ) ( log ( - 4 m sin 2 ( z ) ) + 2 ) - 4 m E ( 1 m ) ( log ( - 4 m sin 2 ( z ) ) + 4 ) ) + 3 8 m 2 sin 2 ( z ) k = 0 ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] ( 5 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "2"], ")"]], "k"], Pochhammer] m - k ( k + 1 ) ! 3 F ~ 2 ( 1 , 1 , k + 5 2 ; k + 4 , 2 ; csc 2 ( z ) m ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["5", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["k", "+", "4"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List[SuperscriptBox["csc", "2"], "(", "z", ")"]], "m"], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] + 9 8 m 2 k = 0 ( 5 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "2"], ")"]], "k"], Pochhammer] 2 m - k ( k + 2 ) ! ( k + 3 ) ! j = 0 k 1 j + k + 3 ) E ( z m ) 2 Re ( z ) π E ( m ) + ( - 1 ) Re ( z ) π - m sin 2 ( z ) 4 m sin ( z ) ( 2 1 - csc 2 ( z ) m m sin 2 ( z ) + 2 m sin 2 ( z ) k = 0 m - k ( 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "k"], Pochhammer] ( - 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "2"]]], ")"]], "k"], Pochhammer] ( k ! ) 2 3 F 2 ( 1 , 1 , k + 1 2 ; 2 , k + 1 ; sin 2 ( z ) ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[SuperscriptBox["sin", "2"], "(", "z", ")"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + 1 8 m 4 F 3 ( 1 , 1 , 3 2 , 3 2 ; 2 , 2 , 3 ; 1 m ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["1", "m"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 2 log ( 1 - csc 2 ( z ) m + 1 ) + 1 π ( π ( cos ( 2 z ) m + 3 m + log ( 4 ) + 1 ) + 4 ( m - 1 ) K ( 1 m ) ( log ( - 4 m sin 2 ( z ) ) + 2 ) - 4 m E ( 1 m ) ( log ( - 4 m sin 2 ( z ) ) + 4 ) ) + 3 8 m 2 sin 2 ( z ) k = 0 ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] ( 5 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "2"], ")"]], "k"], Pochhammer] m - k ( k + 1 ) ! 3 F ~ 2 ( 1 , 1 , k + 5 2 ; k + 4 , 2 ; csc 2 ( z ) m ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", FractionBox["5", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["k", "+", "4"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List[SuperscriptBox["csc", "2"], "(", "z", ")"]], "m"], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] + 9 8 m 2 k = 0 ( 5 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "2"], ")"]], "k"], Pochhammer] 2 m - k ( k + 2 ) ! ( k + 3 ) ! j = 0 k 1 j + k + 3 ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticE", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "m"]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], " ", SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"], "m"]]]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"], "m"]]]]]], "]"]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "2"], ",", "k"]], "]"]], " ", SuperscriptBox["m", RowBox[List["-", "k"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List[FractionBox["5", "2"], "+", "k"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["4", "+", "k"]], ",", "2"]], "}"]], ",", FractionBox[SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"], "m"]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "!"]]]]]]], RowBox[List["8", " ", SuperscriptBox["m", "2"], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["3", " ", "m"]], "+", RowBox[List["m", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["Log", "[", "4", "]"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox["1", "m"], "]"]]]], "-", RowBox[List["4", " ", "m", " ", RowBox[List["EllipticE", "[", FractionBox["1", "m"], "]"]], " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]], ")"]]]]]], "\[Pi]"], "+", FractionBox[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", "3"]], "}"]], ",", FractionBox["1", "m"]]], "]"]], RowBox[List["8", " ", "m"]]], "+", FractionBox[RowBox[List["9", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "2"], ",", "k"]], "]"]], "2"], " ", SuperscriptBox["m", RowBox[List["-", "k"]]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "k"], FractionBox["1", RowBox[List["j", "+", "k", "+", "3"]]]]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "+", "k"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["3", "+", "k"]], ")"]], "!"]]]]]]]]], RowBox[List["8", " ", SuperscriptBox["m", "2"]]]], "+", RowBox[List["2", " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["m", RowBox[List["-", "k"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "k"]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List[FractionBox["1", "2"], "+", "k"]]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", RowBox[List["1", "+", "k"]]]], "}"]], ",", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "2"]]]]]]]], ")"]]]], RowBox[List["4", " ", "m", " ", RowBox[List["Sin", "[", "z", "]"]]]]], "+", RowBox[List["2", " ", RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["EllipticE", "[", "m", "]"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02