Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.adp1)

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=4, b₁>=-11/2

For fixed z and a₁=1/2, a₂=4, b₁=-9/2

http://functions.wolfram.com/07.25.03.adp1.01

Input Form

HypergeometricPFQ[{1/2, 4}, {-(9/2), 9/2}, -z] == (-100800 - 41160 z - 13680 z^2 - 3708 z^3 - 844 z^4 - 165 z^5 - 28 z^6 - 4 z^7)/(108 z^3) + (1/(216 z^(7/2))) ((Sqrt[Pi] (100800 + 108360 z + 59040 z^2 + 21960 z^3 + 6300 z^4 + 1485 z^5 + 298 z^6 + 52 z^7 + 8 z^8) 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]