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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(5/2), -(5/2)}, z] == (1/10125) (10125 + 24300 z + 132300 z^2 + 6350400 z^3 + 235580400 z^4 + 844786800 z^5 + 987189840 z^6 + 524129040 z^7 + 146419470 z^8 + 23088810 z^9 + 2105160 z^10 + 108944 z^11 + 2944 z^12 + 32 z^13) + (1/10125) (E^z Sqrt[Pi] (39382200 z^(7/2) + 459459000 z^(9/2) + 1187433000 z^(11/2) + 1197225000 z^(13/2) + 587982825 z^(15/2) + 157034565 z^(17/2) + 24090450 z^(19/2) + 2158200 z^(21/2) + 110400 z^(23/2) + 2960 z^(25/2) + 32 z^(27/2)) Erf[Sqrt[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]