Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am0i)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.am0i.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(7/2), -(3/2)}, z] == (1/99225) (99225 + 340200 z + 3742200 z^2 - 64864800 z^3 + 1135134000 z^4 + 6815128320 z^5 + 9704298240 z^6 + 5812853760 z^7 + 1773907200 z^8 + 300364800 z^9 + 29097984 z^10 + 1588608 z^11 + 45056 z^12 + 512 z^13) + (1/99225) (64 E^z Sqrt[Pi] (43243200 z^(9/2) + 157248000 z^(11/2) + 187412400 z^(13/2) + 102805920 z^(15/2) + 29864520 z^(17/2) + 4908960 z^(19/2) + 466725 z^(21/2) + 25170 z^(23/2) + 708 z^(25/2) + 8 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]