Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak0u)

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, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ak0u.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(11/2), -(5/2)}, -z] == (1/2338875) (2338875 - 1786050 z + 2381400 z^2 - 12474000 z^3 - 97297200 z^4 - 454053600 z^5 - 4116752640 z^6 + 12940715520 z^7 - 11124691200 z^8 + 4248061440 z^9 - 842250240 z^10 + 91926528 z^11 - 5515264 z^12 + 168960 z^13 - 2048 z^14) + (1/2338875) ((512 Sqrt[Pi] (15422400 z^(13/2) - 33415200 z^(15/2) + 25235280 z^(17/2) - 9041760 z^(19/2) + 1729800 z^(21/2) - 184770 z^(23/2) + 10935 z^(25/2) - 332 z^(27/2) + 4 z^(29/2)) 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]