Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah0j)

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=5, b₁>=-11/2

For fixed z and a₁=3/2, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.ah0j.01

Input Form

HypergeometricPFQ[{3/2, 5}, {-(7/2), -(7/2)}, -z] == (1/33075) (33075 - 20250 z + 24300 z^2 - 88200 z^3 + 3175200 z^4 - 90731520 z^5 + 254280000 z^6 - 233461440 z^7 + 96793920 z^8 - 20746040 z^9 + 2428872 z^10 - 155120 z^11 + 5024 z^12 - 64 z^13) + (1/33075) ((4 Sqrt[Pi] (-4375800 z^(9/2) + 40973400 z^(11/2) - 85037400 z^(13/2) + 68476680 z^(15/2) - 26531145 z^(17/2) + 5472225 z^(19/2) - 626000 z^(21/2) + 39400 z^(23/2) - 1264 z^(25/2) + 16 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]