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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Identities > Recurrence identities > Distant neighbors





http://functions.wolfram.com/07.23.17.0006.01









  


  








Input Form





Hypergeometric2F1[a, b, c, z] == ((Pochhammer[1 - c, m]/Pochhammer[1 - a, m]) Sum[(-1)^k Binomial[m, k] Hypergeometric2F1[a - m, b - k, c - m, z], {k, 0, m}])/z^m /; Element[m, Integers] && m >= 0








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", "c_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "c"]], ",", "m"]], "]"]], " ", SuperscriptBox["z", RowBox[List["-", "m"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "m"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["a", "-", "m"]], ",", RowBox[List["b", "-", "k"]], ",", RowBox[List["c", "-", "m"]], ",", "z"]], "]"]]]]]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "a"]], ",", "m"]], "]"]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2001-10-29