Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aig2)

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=2, a₂>=2

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

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

http://functions.wolfram.com/07.25.03.aig2.01

Input Form

HypergeometricPFQ[{2, 11/2}, {-(5/2), -(5/2)}, -z] == (1/212625) (212625 - 374220 z + 1621620 z^2 - 64864800 z^3 + 2013575760 z^4 - 6040319040 z^5 + 5873781312 z^6 - 2560730112 z^7 + 574060800 z^8 - 70007808 z^9 + 4641792 z^10 - 155648 z^11 + 2048 z^12) - (1/212625) ((1024 Sqrt[Pi] (-362880 z^(7/2) + 3628800 z^(9/2) - 7983360 z^(11/2) + 6773760 z^(13/2) - 2751840 z^(15/2) + 592704 z^(17/2) - 70560 z^(19/2) + 4608 z^(21/2) - 153 z^(23/2) + 2 z^(25/2)) 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]