Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj58)

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=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-9/2

http://functions.wolfram.com/07.25.03.aj58.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(9/2), -(9/2)}, -z] == (1/8037225) (8037225 - 3969000 z + 2835000 z^2 - 4082400 z^3 + 17463600 z^4 - 726485760 z^5 + 24137568000 z^6 - 79264281600 z^7 + 86166662400 z^8 - 43021854720 z^9 + 11392336896 z^10 - 1713331200 z^11 + 149721600 z^12 - 7456256 z^13 + 194560 z^14 - 2048 z^15) + (1/8037225) ((256 Sqrt[Pi] (16707600 z^(11/2) - 178642800 z^(13/2) + 428357160 z^(15/2) - 404578440 z^(17/2) + 187570530 z^(19/2) - 47588310 z^(21/2) + 6971475 z^(23/2) - 599043 z^(25/2) + 29502 z^(27/2) - 764 z^(29/2) + 8 z^(31/2)) Erfi[Sqrt[z]])/E^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]