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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(11/2), -(11/2)}, -z] == (1/24312605625) (24312605625 - 16878172500 z + 13127467500 z^2 - 15717240000 z^3 + 36778341600 z^4 - 245188944000 z^5 + 15283444176000 z^6 - 778215044275200 z^7 + 3999282542841600 z^8 - 6970962530810880 z^9 + 5789095285478400 z^10 - 2684913741619200 z^11 + 759723279114240 z^12 - 138224208568320 z^13 + 16667531993088 z^14 - 1350493804800 z^15 + 73417317120 z^16 - 2626148352 z^17 + 58966016 z^18 - 749568 z^19 + 4096 z^20) - (1/24312605625) ((128 Sqrt[Pi] (849188188800 z^(13/2) - 13303948291200 z^(15/2) + 48087362534400 z^(17/2) - 70919920915200 z^(19/2) + 53669755591200 z^(21/2) - 23527989142560 z^(23/2) + 6421103267040 z^(25/2) - 1140340330080 z^(27/2) + 135227314215 z^(29/2) - 10827810315 z^(31/2) + 583608018 z^(33/2) - 20744232 z^(35/2) + 463584 z^(37/2) - 5872 z^(39/2) + 32 z^(41/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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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]