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; }

 Csch

 http://functions.wolfram.com/01.23.21.0219.01

 Input Form

 Integrate[Sin[a z]^m Coth[c z]^u Csch[c z], z] == -((1/(c + c u)) (2^(1 - m - u) E^(c z) (1 - E^(2 c z))^u Binomial[m, m/2] Binomial[u, u/2] Csch[c z]^u HypergeometricPFQ[{1/2 + u/2, 1 + u}, {3/2 + u/2}, E^(2 c z)] (-1 + Mod[m, 2]) (-1 + Mod[u, 2]))) - 2^(1 - m - u) E^(c z) (1 - E^(2 c z))^u Binomial[u, u/2] Csch[c z]^u (1 - Mod[u, 2]) Sum[(-1)^s Binomial[m, s] ((E^((-(1/2)) I m Pi + I a (m - 2 s) z) HypergeometricPFQ[ {1/2 + (I a m)/(2 c) - (I a s)/c + u/2, 1 + u}, {3/2 + (I a m)/(2 c) - (I a s)/c + u/2}, E^(2 c z)])/ (I a (m - 2 s) + c (1 + u)) + (E^((I m Pi)/2 - I a (m - 2 s) z) HypergeometricPFQ[{1/2 - (I a m)/(2 c) + (I a s)/c + u/2, 1 + u}, {3/2 - (I a m)/(2 c) + (I a s)/c + u/2}, E^(2 c z)])/ ((-I) a (m - 2 s) + c (1 + u))), {s, 0, Floor[(1/2) (-1 + m)]}] - 2^(1 - m - u) E^(c z) (1 - E^(2 c z))^u Binomial[m, m/2] Csch[c z]^u (1 - Mod[m, 2]) Sum[Binomial[u, k] (HypergeometricPFQ[{1/2 + k, 1 + u}, {3/2 + k}, E^(2 c z)]/ E^(c (-2 k + u) z)/(c (1 + u) - c (-2 k + u)) + (1/(c (1 - 2 k + 2 u))) (E^(c (-2 k + u) z) HypergeometricPFQ[ {1 + u, 1/2 - k + u}, {3/2 - k + u}, E^(2 c z)])), {k, 0, Floor[(1/2) (-1 + u)]}] - 2^(1 - m - u) E^(c z) (1 - E^(2 c z))^u Csch[c z]^u Sum[(-1)^s Binomial[m, s] Binomial[u, k] ((E^((-(1/2)) I m Pi + (I a (m - 2 s) - c (-2 k + u)) z) HypergeometricPFQ[{1/2 + k + (I a m)/(2 c) - (I a s)/c, 1 + u}, {3/2 + k + (I a m)/(2 c) - (I a s)/c}, E^(2 c z)])/ (c (1 + 2 k) + I a (m - 2 s)) + (E^((I m Pi)/2 + ((-I) a (m - 2 s) - c (-2 k + u)) z) HypergeometricPFQ[{1/2 + k - (I a m)/(2 c) + (I a s)/c, 1 + u}, {3/2 + k - (I a m)/(2 c) + (I a s)/c}, E^(2 c z)])/ (c (1 + 2 k) - I a (m - 2 s)) + (E^((-(1/2)) I m Pi + (I a (m - 2 s) + c (-2 k + u)) z) HypergeometricPFQ[{1 + u, 1/2 - k + (I a m)/(2 c) - (I a s)/c + u}, {3/2 - k + (I a m)/(2 c) - (I a s)/c + u}, E^(2 c z)])/ (I a (m - 2 s) + c (1 - 2 k + 2 u)) + (E^((I m Pi)/2 + ((-I) a (m - 2 s) + c (-2 k + u)) z) HypergeometricPFQ[{1 + u, 1/2 - k - (I a m)/(2 c) + (I a s)/c + u}, {3/2 - k - (I a m)/(2 c) + (I a s)/c + u}, E^(2 c z)])/ ((-I) a (m - 2 s) + c (1 - 2 k + 2 u))), {k, 0, Floor[(1/2) (-1 + u)]}, {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0

 Standard Form

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RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["u", "\[Element]", "Integers"]], "\[And]", RowBox[List["u", ">", "0"]]]]]]]]

 MathML Form

 sin m ( a z ) coth u ( c z ) csch ( c z ) z - 2 - m - u + 1 c z ( 1 - 2 c z ) u ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["u", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - u mod 2 \$CellContext`u 2 ) ( s = 0 m - 1 2 ( - 1 ) s ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( m π 2 - a ( m - 2 s ) z 2 F 1 ( - a m 2 c + a s c + u 2 + 1 2 , u + 1 ; - a m 2 c + a s c + u 2 + 3 2 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"], "+", FractionBox["u", "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"], "+", FractionBox["u", "2"], "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] c ( u + 1 ) - a ( m - 2 s ) + a ( m - 2 s ) z - m π 2 2 F 1 ( a m 2 c + u 2 + 1 2 - a s c , u + 1 ; a m 2 c + u 2 + 3 2 - a s c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]], "+", FractionBox["u", "2"], "+", FractionBox["1", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]], "+", FractionBox["u", "2"], "+", FractionBox["3", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] a ( m - 2 s ) + c ( u + 1 ) ) ) csch u ( c z ) - 2 - m - u + 1 c z ( 1 - 2 c z ) u ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - m mod 2 \$CellContext`m 2 ) ( k = 0 u - 1 2 ( u k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - c ( u - 2 k ) z 2 F 1 ( k + 1 2 , u + 1 ; k + 3 2 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["k", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["k", "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] c ( u + 1 ) - c ( u - 2 k ) + c ( u - 2 k ) z 2 F 1 ( u + 1 , - k + u + 1 2 ; - k + u + 3 2 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "k"]], "+", "u", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["-", "k"]], "+", "u", "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] c ( - 2 k + 2 u + 1 ) ) ) csch u ( c z ) - 2 - m - u + 1 c z ( 1 - 2 c z ) u ( k = 0 u - 1 2 s = 0 m - 1 2 ( - 1 ) s ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( u k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( π m 2 + ( - a ( m - 2 s ) - c ( u - 2 k ) ) z 2 F 1 ( k + a s c + 1 2 - a m 2 c , u + 1 ; k + a s c + 3 2 - a m 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["k", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"], "+", FractionBox["1", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["k", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"], "+", FractionBox["3", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] c ( 2 k + 1 ) - a ( m - 2 s ) + ( ( a ( m - 2 s ) - c ( u - 2 k ) ) z - m π 2 2 F 1 ( k + a m 2 c + 1 2 - a s c , u + 1 ; k + a m 2 c + 3 2 - a s c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["k", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]], "+", FractionBox["1", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["k", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]], "+", FractionBox["3", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) / ( c ( 2 k + 1 ) + a ( m - 2 s ) ) + ( π m 2 + ( c ( u - 2 k ) - a ( m - 2 s ) ) z 2 F 1 ( u + 1 , - k + a s c + u + 1 2 - a m 2 c ; - k + a s c + u + 3 2 - a m 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "k"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"], "+", "u", "+", FractionBox["1", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["-", "k"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"], "+", "u", "+", FractionBox["3", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) / ( c ( - 2 k + 2 u + 1 ) - a ( m - 2 s ) ) + ( ( a ( m - 2 s ) + c ( u - 2 k ) ) z - m π 2 2 F 1 ( u + 1 , - k + a m 2 c + u + 1 2 - a s c ; - k + a m 2 c + u + 3 2 - a s c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "k"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]], "+", "u", "+", FractionBox["1", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["-", "k"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "m"]], RowBox[List["2", " ", "c"]]], "+", "u", "+", FractionBox["3", "2"], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "s"]], "c"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) / ( a ( m - 2 s ) + c ( - 2 k + 2 u + 1 ) ) ) ) csch u ( c z ) - 1 u c + c ( 2 - m - u + 1 c z ( 1 - 2 c z ) u ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["u", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] csch u ( c z ) 2 F 1 ( u 2 + 1 2 , u + 1 ; u 2 + 3 2 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["u", "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["u", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox["u", "2"], "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ( m mod 2 \$CellContext`m 2 - 1 ) ( u mod 2 \$CellContext`u 2 - 1 ) ) /; m + u + Condition z a z m c z u c z -1 2 -1 m -1 u 1 c z 1 -1 2 c z u Binomial u u 2 -1 1 -1 \$CellContext`u 2 s 0 m -1 2 -1 -1 s Binomial m s m 2 -1 -1 a m -1 2 s z HypergeometricPFQ -1 a m 2 c -1 a s c -1 u 2 -1 1 2 u 1 -1 a m 2 c -1 a s c -1 u 2 -1 3 2 2 c z c u 1 -1 a m -1 2 s -1 a m -1 2 s z -1 m 2 -1 HypergeometricPFQ a m 2 c -1 u 2 -1 1 2 -1 a s c -1 u 1 a m 2 c -1 u 2 -1 3 2 -1 a s c -1 2 c z a m -1 2 s c u 1 -1 c z u -1 2 -1 m -1 u 1 c z 1 -1 2 c z u Binomial m m 2 -1 1 -1 \$CellContext`m 2 k 0 u -1 2 -1 Binomial u k -1 c u -1 2 k z HypergeometricPFQ k 1 2 u 1 k 3 2 2 c z c u 1 -1 c u -1 2 k -1 c u -1 2 k z HypergeometricPFQ u 1 -1 k u 1 2 -1 k u 3 2 2 c z c -2 k 2 u 1 -1 c z u -1 2 -1 m -1 u 1 c z 1 -1 2 c z u s 0 m -1 2 -1 k 0 u -1 2 -1 -1 s Binomial m s Binomial u k m 2 -1 -1 a m -1 2 s -1 c u -1 2 k z HypergeometricPFQ k a s c -1 1 2 -1 a m 2 c -1 u 1 k a s c -1 3 2 -1 a m 2 c -1 2 c z c 2 k 1 -1 a m -1 2 s -1 a m -1 2 s -1 c u -1 2 k z -1 m 2 -1 HypergeometricPFQ k a m 2 c -1 1 2 -1 a s c -1 u 1 k a m 2 c -1 3 2 -1 a s c -1 2 c z c 2 k 1 a m -1 2 s -1 m 2 -1 c u -1 2 k -1 a m -1 2 s z HypergeometricPFQ u 1 -1 k a s c -1 u 1 2 -1 a m 2 c -1 -1 k a s c -1 u 3 2 -1 a m 2 c -1 2 c z c -2 k 2 u 1 -1 a m -1 2 s -1 a m -1 2 s c u -1 2 k z -1 m 2 -1 HypergeometricPFQ u 1 -1 k a m 2 c -1 u 1 2 -1 a s c -1 -1 k a m 2 c -1 u 3 2 -1 a s c -1 2 c z a m -1 2 s c -2 k 2 u 1 -1 c z u -1 1 u c c -1 2 -1 m -1 u 1 c z 1 -1 2 c z u Binomial m m 2 -1 Binomial u u 2 -1 c z u HypergeometricPFQ u 2 -1 1 2 u 1 u 2 -1 3 2 2 c z \$CellContext`m 2 -1 \$CellContext`u 2 -1 m SuperPlus u SuperPlus [/itex]

 Rule Form

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

 2002-12-18