Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa8a)

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=-9/2

http://functions.wolfram.com/07.25.03.aa8a.01

Input Form

HypergeometricPFQ[{-(3/2), 5}, {-(9/2), -(1/2)}, -z] == (3780 + 12600 z + 9990 z^2 + 3570 z^3 - 609 z^4 - 6417 z^5 + 2270 z^6 - 244 z^7 + 8 z^8)/3780 + (1/7560) ((Sqrt[Pi] (-20790 z^(3/2) - 20790 z^(5/2) - 10395 z^(7/2) - 3465 z^(9/2) + 14880 z^(11/2) - 4776 z^(13/2) + 496 z^(15/2) - 16 z^(17/2)) 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]