Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.afb2)

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=9/2, b₁>=-11/2

For fixed z and a₁=1, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.afb2.01

Input Form

HypergeometricPFQ[{1, 9/2}, {-(11/2), -(5/2)}, z] == (1/16372125) (16372125 + 5358150 z + 4365900 z^2 + 16216200 z^3 - 97297200 z^4 + 367567200 z^5 - 2793510720 z^6 - 6852021120 z^7 - 4609032960 z^8 - 1352440320 z^9 - 199111680 z^10 - 15202304 z^11 - 569344 z^12 - 8192 z^13) - (1/16372125) (8192 E^z Sqrt[Pi] (604800 z^(13/2) + 1058400 z^(15/2) + 635040 z^(17/2) + 176400 z^(19/2) + 25200 z^(21/2) + 1890 z^(23/2) + 70 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]