Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aaj3)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.aaj3.01

Input Form

HypergeometricPFQ[{-(3/2), 6}, {-(11/2), 3/2}, z] == (1/831600) (491400 - 226800 z - 17640 z^2 + 48180 z^3 - 21321 z^4 + 4560 z^5 + 3920 z^6 + 480 z^7 + 16 z^8) + (1/(1663200 Sqrt[z])) (E^z Sqrt[Pi] (340200 + 907200 z - 536760 z^2 + 26460 z^3 + 76545 z^4 - 40950 z^5 + 12600 z^6 + 8304 z^7 + 976 z^8 + 32 z^9) 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]