Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1783)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=3, b₁=9/2

http://functions.wolfram.com/07.25.03.1783.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {9/2, 6}, -z] == -((60 (-4 + 42 z + 133 z^2))/(4199 z^5)) + (1/(13002522624 z^5)) ((-743178240 + 7060193280 z + 9226941255 z^2 - 3287685240 z^3 + 2800080360 z^4 + 5707171008 z^5 + 2222298624 z^6 + 368552064 z^7 + 29772672 z^8 + 1144832 z^9 + 16640 z^10)/E^z) + (1/(26005045248 z^(7/2))) (Sqrt[Pi] (22915517625 + 16499172690 z - 6285399120 z^2 + 9777287520 z^3 + 13332664800 z^4 + 4786084800 z^5 + 765773568 z^6 + 60673536 z^7 + 2306304 z^8 + 33280 z^9) 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]