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; }

 Hypergeometric2F1Regularized

 http://functions.wolfram.com/07.24.06.0067.01

 Input Form

 Hypergeometric2F1Regularized[a, b, c, z] \[Proportional] Piecewise[{{((-1)^(a - c) (b - c)!)/(Gamma[a] (b - a)!)/(-z)^b, Element[b - a, Integers] && b - a >= 0 && Element[a - c, Integers] && a - c >= 0}, {Log[-z]/((-z)^a (Gamma[a] (c - a - 1)!)), b == a && !(Element[a - c, Integers] && a - c >= 0)}, {((-1)^(b - c) (a - c)!)/(Gamma[b] (a - b)!)/(-z)^a, Element[a - b, Integers] && a - b >= 0 && Element[b - c, Integers] && b - c >= 0}, {0, Element[-c, Integers] && -c >= 0 && ((Element[-a, Integers] && -a >= 0 && c - a <= 0) || (Element[-b, Integers] && -b >= 0 && c - b <= 0))}, {Gamma[b - a]/(Gamma[b] Gamma[c - a])/(-z)^a, Re[b - a] > 0 || (Element[-c, Integers] && -c >= 0 && Element[-a, Integers] && -a >= 0 && c - a > 0)}, {Gamma[a - b]/(Gamma[a] Gamma[c - b])/(-z)^b, Re[b - a] < 0 || (Element[-c, Integers] && -c >= 0 && Element[-b, Integers] && -b >= 0 && c - b > 0)}}, Gamma[b - a]/(Gamma[b] Gamma[c - a])/(-z)^a + Gamma[a - b]/(Gamma[a] Gamma[c - b])/(-z)^b] /; (Abs[z] -> Infinity)

 Standard Form

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 MathML Form

 2 F ~ 1 ( a , b ; c ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1Regularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["b", Hypergeometric2F1Regularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric2F1Regularized, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric2F1Regularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1Regularized] ( - 1 ) a - c ( b - c ) ! ( - z ) - b Γ ( a ) ( b - a ) ! b - a a - c ( - z ) - a log ( - z ) Γ ( a ) ( c - a - 1 ) ! b a ¬ ( a - c TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] a - c 0 ) ( - 1 ) b - c ( a - c ) ! ( - z ) - a Γ ( b ) ( a - b ) ! a - b b - c 0 - c ( ( - a c - a 0 ) ( - b c - b 0 ) ) Γ ( b - a ) ( - z ) - a Γ ( b ) Γ ( c - a ) Re ( b - a ) > 0 ( - c - a c - a > 0 ) Γ ( a - b ) ( - z ) - b Γ ( a ) Γ ( c - b ) Re ( b - a ) < 0 ( - c - b c - b > 0 ) Γ ( b - a ) ( - z ) - a Γ ( b ) Γ ( c - a ) + Γ ( a - b ) ( - z ) - b Γ ( a ) Γ ( c - b ) True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional Hypergeometric2F1Regularized a b c z -1 a -1 c b -1 c -1 z -1 b Gamma a b -1 a -1 b -1 a a -1 c -1 z -1 a -1 z Gamma a c -1 a -1 -1 b a a -1 c a -1 c 0 -1 b -1 c a -1 c -1 z -1 a Gamma b a -1 b -1 a -1 b b -1 c 0 -1 c -1 a c -1 a 0 -1 b c -1 b 0 Gamma b -1 a -1 z -1 a Gamma b Gamma c -1 a -1 b -1 a 0 -1 c -1 a c -1 a 0 Gamma a -1 b -1 z -1 b Gamma a Gamma c -1 b -1 b -1 a 0 -1 c -1 b c -1 b 0 Gamma b -1 a -1 z -1 a Gamma b Gamma c -1 a -1 Gamma a -1 b -1 z -1 b Gamma a Gamma c -1 b -1 Rule z [/itex]

 Rule Form

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

 2007-05-02