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

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=-1/2

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

Input Form

HypergeometricPFQ[{6, 6}, {-(1/2), 1}, -z] == (1/3686400) (3686400 + 265420800 z - 4473757575 z^2 + 13243016850 z^3 - 14458525920 z^4 + 7514784480 z^5 - 2100911840 z^6 + 335478720 z^7 - 31185920 z^8 + 1652224 z^9 - 45824 z^10 + 512 z^11) + (1/7372800) ((Sqrt[Pi] (-2029052025 z^(3/2) + 16232416200 z^(5/2) - 36605754900 z^(7/2) + 34943251200 z^(9/2) - 16859575200 z^(11/2) + 4509845760 z^(13/2) - 700600960 z^(15/2) + 63979520 z^(17/2) - 3349760 z^(19/2) + 92160 z^(21/2) - 1024 z^(23/2)) 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]