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

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=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 3}, {-(11/2), 7/2}, z] == (1/(2079 z^2)) (-967680 + 322560 z - 94689 z^2 + 22230 z^3 - 4200 z^4 + 624 z^5 - 48 z^6 - 32 z^7 + 104 z^8 + 16 z^9) + (1/(2079 z^(5/2))) (4 E^z Sqrt[Pi] (120960 - 120960 z + 60480 z^2 - 20160 z^3 + 5040 z^4 - 1008 z^5 + 168 z^6 - 24 z^7 + 3 z^8 + 28 z^9 + 4 z^10) 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]