Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2311)

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=9/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=9/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.2311.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {-(1/2), 11/2}, -z] == (1/(245760 z^4)) ((-155925 - 103950 z - 41580 z^2 - 11880 z^3 + 243120 z^4 - 1966560 z^5 - 3858240 z^6 - 1604992 z^7 - 220672 z^8 - 9216 z^9)/E^z) + (1/(491520 z^(9/2))) (Sqrt[Pi] (155925 - 6652800 z^6 - 9123840 z^7 - 3421440 z^8 - 450560 z^9 - 18432 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]