Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aju8)

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=-3/2

http://functions.wolfram.com/07.25.03.aju8.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(3/2), -(3/2)}, z] == (1/810) (810 + 5400 z + 264600 z^2 + 9457560 z^3 + 31553280 z^4 + 33389928 z^5 + 15621840 z^6 + 3722265 z^7 + 479052 z^8 + 33336 z^9 + 1168 z^10 + 16 z^11) + (1/1620) (E^z Sqrt[Pi] (3243240 z^(5/2) + 36138960 z^(7/2) + 86949720 z^(9/2) + 79616160 z^(11/2) + 34560135 z^(13/2) + 7893018 z^(15/2) + 990312 z^(17/2) + 67824 z^(19/2) + 2352 z^(21/2) + 32 z^(23/2)) 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]