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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(9/2), -(7/2)}, -z] == (1/1488375) (1488375 - 850500 z + 850500 z^2 - 2116800 z^3 + 28576800 z^4 + 1257379200 z^5 - 12359692800 z^6 + 23859662400 z^7 - 18253560960 z^8 + 6982299360 z^9 - 1488569040 z^10 + 186218760 z^11 - 13853920 z^12 + 597696 z^13 - 13696 z^14 + 128 z^15) - (1/1488375) ((4 Sqrt[Pi] (952333200 z^(11/2) - 4944807000 z^(13/2) + 7683782400 z^(15/2) - 5295168900 z^(17/2) + 1912078350 z^(19/2) - 393859515 z^(21/2) + 48215850 z^(23/2) - 3536520 z^(25/2) + 151120 z^(27/2) - 3440 z^(29/2) + 32 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]