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

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.aaip.01

Input Form

HypergeometricPFQ[{-(3/2), 6}, {-(11/2), -(11/2)}, -z] == (1/540280125) (540280125 + 160744500 z + 13891500 z^2 - 1512000 z^3 + 816480 z^4 - 1814400 z^5 + 46569600 z^6 - 987698880 z^7 + 2113655040 z^8 - 1517538624 z^9 + 500941440 z^10 - 86757000 z^11 + 8313056 z^12 - 439488 z^13 + 11904 z^14 - 128 z^15) + (1/540280125) ((4 Sqrt[Pi] (-56163240 z^(13/2) + 411863760 z^(15/2) - 675060120 z^(17/2) + 433308960 z^(19/2) - 135165135 z^(21/2) + 22677018 z^(23/2) - 2131752 z^(25/2) + 111344 z^(27/2) - 2992 z^(29/2) + 32 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]