Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ac4h)

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=-1/2, a₂>=-1/2

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

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

http://functions.wolfram.com/07.25.03.ac4h.01

Input Form

HypergeometricPFQ[{-(1/2), 5}, {-(11/2), -(11/2)}, -z] == (1/324168075) (324168075 + 26790750 z - 1984500 z^2 + 567000 z^3 - 453600 z^4 + 1270080 z^5 - 38102400 z^6 + 926553600 z^7 - 2243888640 z^8 + 1802707200 z^9 - 659950848 z^10 + 125787360 z^11 - 13174560 z^12 + 756672 z^13 - 22144 z^14 + 256 z^15) - (1/324168075) ((16 Sqrt[Pi] (-12209400 z^(13/2) + 100117080 z^(15/2) - 182853720 z^(17/2) + 130200840 z^(19/2) - 44819145 z^(21/2) + 8251425 z^(23/2) - 846384 z^(25/2) + 47976 z^(27/2) - 1392 z^(29/2) + 16 z^(31/2)) Erfi[Sqrt[z]])/E^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]