Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.acj3)

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=6, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.acj3.01

Input Form

HypergeometricPFQ[{-(1/2), 6}, {-(3/2), 1/2}, -z] == (2880 - 1125 z - 23415 z^2 + 19488 z^3 - 5040 z^4 + 496 z^5 - 16 z^6)/2880 + (1/5760) ((Sqrt[Pi] (-10395 Sqrt[z] - 10395 z^(3/2) + 62370 z^(5/2) - 43560 z^(7/2) + 10560 z^(9/2) - 1008 z^(11/2) + 32 z^(13/2)) 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]