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

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=3, a₂>=3

For fixed z and a₁=3, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(7/2), -(1/2)}, z] == (1/99225) (99225 + 935550 z - 9729720 z^2 + 54054000 z^3 - 551350800 z^4 - 1976214240 z^5 - 1881035520 z^6 - 782756352 z^7 - 167258880 z^8 - 19509760 z^9 - 1242624 z^10 - 40192 z^11 - 512 z^12) - (1/99225) (128 E^z Sqrt[Pi] (8648640 z^(9/2) + 20835360 z^(11/2) + 17251920 z^(13/2) + 6703200 z^(15/2) + 1378440 z^(17/2) + 157122 z^(19/2) + 9863 z^(21/2) + 316 z^(23/2) + 4 z^(25/2)) Erf[Sqrt[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]