Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.af1e)

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=1, a₂>=1

For fixed z and a₁=1, a₂=7/2, b₁>=-11/2

For fixed z and a₁=1, a₂=7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.af1e.01

Input Form

HypergeometricPFQ[{1, 7/2}, {-(9/2), -(9/2)}, z] == (1/13395375) (13395375 + 2315250 z + 850500 z^2 + 748440 z^3 + 2162160 z^4 + 64864800 z^5 + 1544800320 z^6 + 3586477440 z^7 + 2695843584 z^8 + 895013376 z^9 + 148096000 z^10 + 12589056 z^11 + 520192 z^12 + 8192 z^13) + (1/13395375) (8192 E^z Sqrt[Pi] (40320 z^(11/2) + 322560 z^(13/2) + 564480 z^(15/2) + 376320 z^(17/2) + 117600 z^(19/2) + 18816 z^(21/2) + 1568 z^(23/2) + 64 z^(25/2) + z^(27/2)) 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]