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; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.22.06.0011.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1]}, {Subscript[b, 1], Subscript[b, 2]}, z] \[Proportional] ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]])/ (Sqrt[Pi] Gamma[Subscript[a, 1]])) (-z)^((1/2) (1/2 + Subscript[a, 1] - Subscript[b, 1] - Subscript[b, 2])) (Cos[2 Sqrt[-z] + (1/2) Pi (1/2 + Subscript[a, 1] - Subscript[b, 1] - Subscript[b, 2])] (1 + (1/(512 z)) (-15 + 144 Subscript[a, 1]^4 + 16 Subscript[b, 1]^4 + 16 Subscript[b, 2] + 56 Subscript[b, 2]^2 - 64 Subscript[b, 2]^3 + 16 Subscript[b, 2]^4 - 64 Subscript[b, 1]^3 (1 + Subscript[b, 2]) - 64 Subscript[a, 1]^3 (7 + 3 Subscript[b, 1] + 3 Subscript[b, 2]) + 8 Subscript[b, 1]^2 (7 + 8 Subscript[b, 2] + 12 Subscript[b, 2]^2) + 16 Subscript[b, 1] (1 + 25 Subscript[b, 2] + 4 Subscript[b, 2]^2 - 4 Subscript[b, 2]^3) - 8 Subscript[a, 1]^2 (-43 + 4 Subscript[b, 1]^2 - 72 Subscript[b, 2] + 4 Subscript[b, 2]^2 - 8 Subscript[b, 1] (9 + 5 Subscript[b, 2])) + 16 Subscript[a, 1] (-1 + 4 Subscript[b, 1]^3 - 25 Subscript[b, 2] - 4 Subscript[b, 2]^2 + 4 Subscript[b, 2]^3 - 4 Subscript[b, 1]^2 (1 + Subscript[b, 2]) - Subscript[b, 1] (25 + 40 Subscript[b, 2] + 4 Subscript[b, 2]^2))) + \[Ellipsis]) + (1/(8 Sqrt[-z])) Sin[2 Sqrt[-z] + (1/2) Pi (1/2 + Subscript[a, 1] - Subscript[b, 1] - Subscript[b, 2])] (-3 + 12 Subscript[a, 1]^2 - 4 Subscript[b, 1]^2 + 8 Subscript[b, 2] - 4 Subscript[b, 2]^2 + 8 Subscript[b, 1] (1 + Subscript[b, 2]) - 8 Subscript[a, 1] (1 + Subscript[b, 1] + Subscript[b, 2]) + (1/(1536 z)) (-315 + 1728 Subscript[a, 1]^6 - 64 Subscript[b, 1]^6 + 216 Subscript[b, 2] + 1364 Subscript[b, 2]^2 - 960 Subscript[b, 2]^3 - 400 Subscript[b, 2]^4 + 384 Subscript[b, 2]^5 - 64 Subscript[b, 2]^6 + 384 Subscript[b, 1]^5 (1 + Subscript[b, 2]) - 1152 Subscript[a, 1]^5 (11 + 3 Subscript[b, 1] + 3 Subscript[b, 2]) - 16 Subscript[b, 1]^4 (25 + 72 Subscript[b, 2] + 60 Subscript[b, 2]^2) + 64 Subscript[b, 1]^3 (-15 - 71 Subscript[b, 2] + 12 Subscript[b, 2]^2 + 20 Subscript[b, 2]^3) + Subscript[b, 1]^2 (1364 + 13248 Subscript[b, 2] + 9888 Subscript[b, 2]^2 + 768 Subscript[b, 2]^3 - 960 Subscript[b, 2]^4) + 8 Subscript[b, 1] (27 + 2155 Subscript[b, 2] + 1656 Subscript[b, 2]^2 - 568 Subscript[b, 2]^3 - 144 Subscript[b, 2]^4 + 48 Subscript[b, 2]^5) + 48 Subscript[a, 1]^4 (693 + 12 Subscript[b, 1]^2 + 488 Subscript[b, 2] + 12 Subscript[b, 2]^2 + 8 Subscript[b, 1] (61 + 21 Subscript[b, 2])) + 64 Subscript[a, 1]^3 (-585 + 28 Subscript[b, 1]^3 - 853 Subscript[b, 2] - 108 Subscript[b, 2]^2 + 28 Subscript[b, 2]^3 - 12 Subscript[b, 1]^2 (9 + 5 Subscript[b, 2]) - Subscript[b, 1] (853 + 696 Subscript[b, 2] + 60 Subscript[b, 2]^2)) - 12 Subscript[a, 1]^2 (-1323 + 16 Subscript[b, 1]^4 - 4304 Subscript[b, 2] - 1432 Subscript[b, 2]^2 + 448 Subscript[b, 2]^3 + 16 Subscript[b, 2]^4 + 64 Subscript[b, 1]^3 (7 + 3 Subscript[b, 2]) - 8 Subscript[b, 1]^2 (179 + 184 Subscript[b, 2] + 52 Subscript[b, 2]^2) + 16 Subscript[b, 1] (-269 - 449 Subscript[b, 2] - 92 Subscript[b, 2]^2 + 12 Subscript[b, 2]^3)) - 8 Subscript[a, 1] (27 + 48 Subscript[b, 1]^5 + 2155 Subscript[b, 2] + 1656 Subscript[b, 2]^2 - 568 Subscript[b, 2]^3 - 144 Subscript[b, 2]^4 + 48 Subscript[b, 2]^5 - 144 Subscript[b, 1]^4 (1 + Subscript[b, 2]) + 8 Subscript[b, 1]^3 (-71 - 72 Subscript[b, 2] + 12 Subscript[b, 2]^2) + 24 Subscript[b, 1]^2 (69 + 141 Subscript[b, 2] + 60 Subscript[b, 2]^2 + 4 Subscript[b, 2]^3) + Subscript[b, 1] (2155 + 8112 Subscript[b, 2] + 3384 Subscript[b, 2]^2 - 576 Subscript[b, 2]^3 - 144 Subscript[b, 2]^4))) + \[Ellipsis])) /; (Abs[z] -> Infinity)

 Standard Form

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 MathML Form

 1 F 2 ( a 1 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], 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] Γ ( b 1 ) Γ ( b 2 ) π Γ ( a 1 ) ( - z ) 1 2 ( a 1 - b 1 - b 2 + 1 2 ) ( ( 1 + 1 512 z ( 144 a 1 4 - 64 ( 3 b 1 + 3 b 2 + 7 ) a 1 3 - 8 ( 4 b 1 2 - 8 ( 5 b 2 + 9 ) b 1 + 4 b 2 2 - 72 b 2 - 43 ) a 1 2 + 16 ( 4 b 1 3 - 4 ( b 2 + 1 ) b 1 2 - ( 4 b 2 2 + 40 b 2 + 25 ) b 1 + 4 b 2 3 - 4 b 2 2 - 25 b 2 - 1 ) a 1 + 16 b 1 4 + 16 b 2 4 - 64 b 2 3 + 56 b 2 2 + 16 b 2 - 64 b 1 3 ( b 2 + 1 ) + 8 b 1 2 ( 12 b 2 2 + 8 b 2 + 7 ) + 16 b 1 ( - 4 b 2 3 + 4 b 2 2 + 25 b 2 + 1 ) - 15 ) + ) cos ( π 2 ( a 1 - b 1 - b 2 + 1 2 ) + 2 - z ) + 1 8 - z ( - 3 + 12 a 1 2 - 4 b 1 2 + 8 b 2 - 4 b 2 2 + 8 b 1 ( 1 + b 2 ) - 8 a 1 ( 1 + b 1 + b 2 ) + 1 1536 z ( 1728 a 1 6 - 1152 ( 3 b 1 + 3 b 2 + 11 ) a 1 5 + 48 ( 12 b 1 2 + 8 ( 21 b 2 + 61 ) b 1 + 12 b 2 2 + 488 b 2 + 693 ) a 1 4 + 64 ( 28 b 1 3 - 12 ( 5 b 2 + 9 ) b 1 2 - ( 60 b 2 2 + 696 b 2 + 853 ) b 1 + 28 b 2 3 - 108 b 2 2 - 853 b 2 - 585 ) a 1 3 - 12 ( 16 b 1 4 + 64 ( 3 b 2 + 7 ) b 1 3 - 8 ( 52 b 2 2 + 184 b 2 + 179 ) b 1 2 + 16 ( 12 b 2 3 - 92 b 2 2 - 449 b 2 - 269 ) b 1 + 16 b 2 4 + 448 b 2 3 - 1432 b 2 2 - 4304 b 2 - 1323 ) a 1 2 - 8 ( 48 b 1 5 - 144 ( b 2 + 1 ) b 1 4 + 8 ( 12 b 2 2 - 72 b 2 - 71 ) b 1 3 + 24 ( 4 b 2 3 + 60 b 2 2 + 141 b 2 + 69 ) b 1 2 + ( - 144 b 2 4 - 576 b 2 3 + 3384 b 2 2 + 8112 b 2 + 2155 ) b 1 + 48 b 2 5 - 144 b 2 4 - 568 b 2 3 + 1656 b 2 2 + 2155 b 2 + 27 ) a 1 - 64 b 1 6 - 64 b 2 6 + 384 b 2 5 - 400 b 2 4 - 960 b 2 3 + 1364 b 2 2 + 216 b 2 + 384 b 1 5 ( b 2 + 1 ) - 16 b 1 4 ( 60 b 2 2 + 72 b 2 + 25 ) + 64 b 1 3 ( 20 b 2 3 + 12 b 2 2 - 71 b 2 - 15 ) + b 1 2 ( - 960 b 2 4 + 768 b 2 3 + 9888 b 2 2 + 13248 b 2 + 1364 ) + 8 b 1 ( 48 b 2 5 - 144 b 2 4 - 568 b 2 3 + 1656 b 2 2 + 2155 b 2 + 27 ) - 315 ) + ) sin ( π 2 ( a 1 - b 1 - b 2 + 1 2 ) + 2 - z ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional HypergeometricPFQ Subscript a 1 Subscript b 1 Subscript b 2 z Gamma Subscript b 1 Gamma Subscript b 2 1 2 Gamma Subscript a 1 -1 -1 z 1 2 Subscript a 1 -1 Subscript b 1 -1 Subscript b 2 1 2 1 1 512 z -1 144 Subscript a 1 4 -1 64 3 Subscript b 1 3 Subscript b 2 7 Subscript a 1 3 -1 8 4 Subscript b 1 2 -1 8 5 Subscript b 2 9 Subscript b 1 4 Subscript b 2 2 -1 72 Subscript b 2 -43 Subscript a 1 2 16 4 Subscript b 1 3 -1 4 Subscript b 2 1 Subscript b 1 2 -1 4 Subscript b 2 2 40 Subscript b 2 25 Subscript b 1 4 Subscript b 2 3 -1 4 Subscript b 2 2 -1 25 Subscript b 2 -1 Subscript a 1 16 Subscript b 1 4 16 Subscript b 2 4 -1 64 Subscript b 2 3 56 Subscript b 2 2 16 Subscript b 2 -1 64 Subscript b 1 3 Subscript b 2 1 8 Subscript b 1 2 12 Subscript b 2 2 8 Subscript b 2 7 16 Subscript b 1 -4 Subscript b 2 3 4 Subscript b 2 2 25 Subscript b 2 1 -15 2 -1 Subscript a 1 -1 Subscript b 1 -1 Subscript b 2 1 2 2 -1 z 1 2 1 8 -1 z 1 2 -1 -3 12 Subscript a 1 2 -1 4 Subscript b 1 2 8 Subscript b 2 -1 4 Subscript b 2 2 8 Subscript b 1 1 Subscript b 2 -1 8 Subscript a 1 1 Subscript b 1 Subscript b 2 1 1536 z -1 1728 Subscript a 1 6 -1 1152 3 Subscript b 1 3 Subscript b 2 11 Subscript a 1 5 48 12 Subscript b 1 2 8 21 Subscript b 2 61 Subscript b 1 12 Subscript b 2 2 488 Subscript b 2 693 Subscript a 1 4 64 28 Subscript b 1 3 -1 12 5 Subscript b 2 9 Subscript b 1 2 -1 60 Subscript b 2 2 696 Subscript b 2 853 Subscript b 1 28 Subscript b 2 3 -1 108 Subscript b 2 2 -1 853 Subscript b 2 -585 Subscript a 1 3 -1 12 16 Subscript b 1 4 64 3 Subscript b 2 7 Subscript b 1 3 -1 8 52 Subscript b 2 2 184 Subscript b 2 179 Subscript b 1 2 16 12 Subscript b 2 3 -1 92 Subscript b 2 2 -1 449 Subscript b 2 -269 Subscript b 1 16 Subscript b 2 4 448 Subscript b 2 3 -1 1432 Subscript b 2 2 -1 4304 Subscript b 2 -1323 Subscript a 1 2 -1 8 48 Subscript b 1 5 -1 144 Subscript b 2 1 Subscript b 1 4 8 12 Subscript b 2 2 -1 72 Subscript b 2 -71 Subscript b 1 3 24 4 Subscript b 2 3 60 Subscript b 2 2 141 Subscript b 2 69 Subscript b 1 2 -144 Subscript b 2 4 -1 576 Subscript b 2 3 3384 Subscript b 2 2 8112 Subscript b 2 2155 Subscript b 1 48 Subscript b 2 5 -1 144 Subscript b 2 4 -1 568 Subscript b 2 3 1656 Subscript b 2 2 2155 Subscript b 2 27 Subscript a 1 -1 64 Subscript b 1 6 -1 64 Subscript b 2 6 384 Subscript b 2 5 -1 400 Subscript b 2 4 -1 960 Subscript b 2 3 1364 Subscript b 2 2 216 Subscript b 2 384 Subscript b 1 5 Subscript b 2 1 -1 16 Subscript b 1 4 60 Subscript b 2 2 72 Subscript b 2 25 64 Subscript b 1 3 20 Subscript b 2 3 12 Subscript b 2 2 -1 71 Subscript b 2 -15 Subscript b 1 2 -960 Subscript b 2 4 768 Subscript b 2 3 9888 Subscript b 2 2 13248 Subscript b 2 1364 8 Subscript b 1 48 Subscript b 2 5 -1 144 Subscript b 2 4 -1 568 Subscript b 2 3 1656 Subscript b 2 2 2155 Subscript b 2 27 -315 2 -1 Subscript a 1 -1 Subscript b 1 -1 Subscript b 2 1 2 2 -1 z 1 2 Rule z [/itex]

 Rule Form

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

 2001-10-29