Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.add8)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=3, b₁>=-11/2

For fixed z and a₁=1/2, a₂=3, b₁=-9/2

http://functions.wolfram.com/07.25.03.add8.01

Input Form

HypergeometricPFQ[{1/2, 3}, {-(9/2), -(9/2)}, -z] == (1/893025) (893025 - 66150 z + 16200 z^2 - 10800 z^3 + 25200 z^4 - 635040 z^5 + 12637440 z^6 - 24184320 z^7 + 14664960 z^8 - 3786240 z^9 + 457984 z^10 - 25344 z^11 + 512 z^12) - (1/893025) ((128 Sqrt[Pi] (-23400 z^(11/2) + 160200 z^(13/2) - 235080 z^(15/2) + 127800 z^(17/2) - 31275 z^(19/2) + 3675 z^(21/2) - 200 z^(23/2) + 4 z^(25/2)) 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]