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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 3}, {-(11/2), -(7/2)}, z] == (1/3274425) (3274425 + 1275750 z + 793800 z^2 + 1134000 z^3 + 7484400 z^4 - 90810720 z^5 + 1210809600 z^6 + 5321756160 z^7 + 5695223040 z^8 + 2567523840 z^9 + 582064128 z^10 + 71086080 z^11 + 4698112 z^12 + 156672 z^13 + 2048 z^14) + (1/3274425) (512 E^z Sqrt[Pi] (5140800 z^(13/2) + 14394240 z^(15/2) + 13199760 z^(17/2) + 5523840 z^(19/2) + 1202040 z^(21/2) + 143280 z^(23/2) + 9327 z^(25/2) + 308 z^(27/2) + 4 z^(29/2)) 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]