Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a9fh)

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=2, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=2, b₁=7/2

http://functions.wolfram.com/07.25.03.a9fh.01

Input Form

HypergeometricPFQ[{-(3/2), 2}, {7/2, 6}, z] == (20 (-24 - 78 z - 286 z^2 + 429 z^3))/(1001 z^5) - (5 E^z (-1152 - 2592 z - 10560 z^2 + 5613 z^3 + 1434 z^4 - 604 z^5 + 40 z^6))/(12012 z^5) + (5 Sqrt[Pi] (-27027 + 10296 z + 3432 z^2 - 1248 z^3 + 80 z^4) Erfi[Sqrt[z]])/(24024 z^(5/2))

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]