Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an3u)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.an3u.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(3/2), 1/2}, z] == (1/9450) (9450 - 340200 z + 8731800 z^2 + 72432360 z^3 + 129729600 z^4 + 93153060 z^5 + 33048600 z^6 + 6367545 z^7 + 690828 z^8 + 41720 z^9 + 1296 z^10 + 16 z^11) + (1/18900) (E^z Sqrt[Pi] (48648600 z^(5/2) + 227026800 z^(7/2) + 330630300 z^(9/2) + 214381440 z^(11/2) + 71866935 z^(13/2) + 13387290 z^(15/2) + 1422120 z^(17/2) + 84720 z^(19/2) + 2608 z^(21/2) + 32 z^(23/2)) 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]