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

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=-11/2

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

Input Form

HypergeometricPFQ[{6, 6}, {-(11/2), 4}, -z] == (1/24948000) (24948000 + 40824000 z + 44452800 z^2 + 45158400 z^3 + 52254720 z^4 + 87091200 z^5 + 390297600 z^6 - 475510635 z^7 + 190037640 z^8 - 36314236 z^9 + 3702720 z^10 - 204880 z^11 + 5760 z^12 - 64 z^13) + (1/49896000) ((Sqrt[Pi] (-1130285205 z^(13/2) + 1112344170 z^(15/2) - 413148540 z^(17/2) + 76140120 z^(19/2) - 7604720 z^(21/2) + 415456 z^(23/2) - 11584 z^(25/2) + 128 z^(27/2)) 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]