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 HypergeometricPFQ

 http://functions.wolfram.com/07.22.03.0314.01

 Input Form

 HypergeometricPFQ[{1 + j}, {1/2 - m, 1/2 - n}, z] == ((-1)^(j + n)/(j! Pochhammer[1/2, n] Pochhammer[1/2, m])) Sum[Binomial[j, i] Pochhammer[1/2 - j - m, -i + j] Sum[Binomial[i + m, k] Pochhammer[-1 - n, i - k + m] ((-1)^n (1 - 2 k - 2 m - 2 n) Pochhammer[-(1/2), k + n] + (-1)^k Pi (k m + m n + z) z^((1/2) (-1 + k + n)) StruveL[-k - n, 2 Sqrt[z]] - (-1)^k m Pi z^((k + n)/2) StruveL[1 - k - n, 2 Sqrt[z]]), {k, 0, i + m}], {i, 0, j}] /; Element[j, Integers] && j >= 0 && Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 1 F 2 ( j + 1 ; 1 2 - m , 1 2 - n ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "1"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["j", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "2"], "-", "m"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", "n"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ( - 1 ) j + n j ! ( 1 2 ) n TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "n"], Pochhammer] ( 1 2 ) m TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "m"], Pochhammer] i = 0 j ( j i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 2 - j - m ) j - i TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "j", "-", "m"]], ")"]], RowBox[List["j", "-", "i"]]], Pochhammer] k = 0 i + m ( i + m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["i", "+", "m"]], Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - n - 1 ) i - k + m TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "n"]], "-", "1"]], ")"]], RowBox[List["i", "-", "k", "+", "m"]]], Pochhammer] ( - ( - 1 ) k m π z k + n 2 L StruveL - k - n + 1 ( 2 z ) + ( - 1 ) k π ( k m + n m + z ) z 1 2 ( k + n - 1 ) L StruveL - k - n ( 2 z ) + ( - 1 ) n ( - 2 k - 2 m - 2 n + 1 ) ( - 1 2 ) k + n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "2"]]], ")"]], RowBox[List["k", "+", "n"]]], Pochhammer] ) /; j m n Condition HypergeometricPFQ j 1 1 2 -1 m 1 2 -1 n z -1 j n j Pochhammer 1 2 n Pochhammer 1 2 m -1 i 0 j Binomial j i Pochhammer 1 2 -1 j -1 m j -1 i k 0 i m Binomial i m k Pochhammer -1 n -1 i -1 k m -1 -1 k m z k n 2 -1 StruveL -1 k -1 n 1 2 z 1 2 -1 k k m n m z z 1 2 k n -1 StruveL -1 k -1 n 2 z 1 2 -1 n -2 k -1 2 m -1 2 n 1 Pochhammer -1 1 2 k n j m n [/itex]

 Rule Form

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 Contributed by

 Brychkov Yu.A. (2006)

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

 2007-05-02