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

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=-11/2

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

Input Form

HypergeometricPFQ[{-(1/2), 4}, {-(11/2), 3/2}, -z] == (9585 + 10440 z + 5400 z^2 + 1800 z^3 + 420 z^4 + 46 z^5 - 96 z^6 + 8 z^7)/ 31185 + (1/(31185 Sqrt[z])) ((Sqrt[Pi] (10800 - 1800 z - 7200 z^2 - 4500 z^3 - 1650 z^4 - 435 z^5 - 90 z^6 + 100 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]