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

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.anrf.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 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)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 840696306912000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 93410700768000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </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]