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

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=6, a₂>=6

For fixed z and a₁=6, a₂=6, b₁>=-11/2

For fixed z and a₁=6, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{6, 6}, {-(9/2), 4}, z] == (1/4536000) (4536000 - 9072000 z + 12700800 z^2 - 18063360 z^3 + 34836480 z^4 - 174182400 z^5 - 252843885 z^6 - 116162460 z^7 - 25034028 z^8 - 2840096 z^9 - 173040 z^10 - 5312 z^11 - 64 z^12) + (1/9072000) (E^z Sqrt[Pi] (-527751315 z^(11/2) - 602533890 z^(13/2) - 254905140 z^(15/2) - 52747800 z^(17/2) - 5848080 z^(19/2) - 351328 z^(21/2) - 10688 z^(23/2) - 128 z^(25/2)) 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]