Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anre)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.anre.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), -(9/2)}, z] == (1/139244923125) (139244923125 + 185659897500 z + 268175407500 z^2 + 612972360000 z^3 + 3126159036000 z^4 + 79196028912000 z^5 - 6098094226224000 z^6 - 112466483724672000 z^7 - 405931768637472000 z^8 - 592657561573862400 z^9 - 448889550012288000 z^10 - 200136549924864000 z^11 - 56566513730764800 z^12 - 10613246928076800 z^13 - 1359839202140160 z^14 - 120802619427840 z^15 - 7468375864320 z^16 - 318593149440 z^17 - 9149982720 z^18 - 168136704 z^19 - 1777664 z^20 - 8192 z^21) - (1/139244923125) (256 E^z Sqrt[Pi] (93410700768000 z^(13/2) + 840696306912000 z^(15/2) + 2327025398544000 z^(17/2) + 2960993895552000 z^(19/2) + 2068699985352000 z^(21/2) + 876504999585600 z^(23/2) + 239514356743200 z^(25/2) + 43909410560400 z^(27/2) + 5534631783450 z^(29/2) + 485891440650 z^(31/2) + 29778513975 z^(33/2) + 1262055690 z^(35/2) + 36067080 z^(37/2) + 660240 z^(39/2) + 6960 z^(41/2) + 32 z^(43/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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</ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]