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

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=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3, 9/2}, {-(7/2), -(3/2)}, -z] == (1/33075) (33075 - 85050 z + 748440 z^2 + 10810800 z^3 + 162162000 z^4 - 805764960 z^5 + 951525120 z^6 - 467034624 z^7 + 114190080 z^8 - 14932480 z^9 + 1050624 z^10 - 37120 z^11 + 512 z^12) - (1/33075) ((128 Sqrt[Pi] (2882880 z^(9/2) - 8910720 z^(11/2) + 8925840 z^(13/2) - 4045440 z^(15/2) + 946680 z^(17/2) - 120624 z^(19/2) + 8351 z^(21/2) - 292 z^(23/2) + 4 z^(25/2)) 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]