Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2472)

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=5, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁=-1/2

http://functions.wolfram.com/07.25.03.2472.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {-(1/2), 6}, -z] == 3960/(4199 z^5) + (1/(4232592 z^5)) ((-3991680 - 3991680 z - 1995840 z^2 - 665280 z^3 - 166320 z^4 + 4199328 z^5 - 34571712 z^6 - 68820141 z^7 - 28894710 z^8 - 4000100 z^9 - 167960 z^10)/E^z) + (1/8465184) (Sqrt[Pi] (-117515475 z^(3/2) - 162954792 z^(5/2) - 61621560 z^(7/2) - 8168160 z^(9/2) - 335920 z^(11/2)) 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]