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

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=6, a₂>=6

For fixed z and a₁=6, a₂=6, b₁>=-11/2

For fixed z and a₁=6, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{6, 6}, {-(5/2), 4}, z] == (1/288000) (288000 - 1036800 z + 3386880 z^2 - 24084480 z^3 - 55658745 z^4 - 36353220 z^5 - 10509580 z^6 - 1538016 z^7 - 117424 z^8 - 4416 z^9 - 64 z^10) + (1/576000) (E^z Sqrt[Pi] (-83687175 z^(7/2) - 140098530 z^(9/2) - 81933540 z^(11/2) - 22450200 z^(13/2) - 3189200 z^(15/2) - 239200 z^(17/2) - 8896 z^(19/2) - 128 z^(21/2)) 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]