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

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, a₂>=3

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

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

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(11/2), -(9/2)}, z] == (1/9282994875) (9282994875 + 6188663250 z + 5108103000 z^2 + 7297290000 z^3 + 24810786000 z^4 + 439977938400 z^5 - 24638764550400 z^6 - 318966446937600 z^7 - 812042351366400 z^8 - 830017724659200 z^9 - 433450290493440 z^10 - 130197232373760 z^11 - 24006284144640 z^12 - 2812060016640 z^13 - 211733053440 z^14 - 10140352512 z^15 - 296583168 z^16 - 4800512 z^17 - 32768 z^18) - (1/9282994875) (8192 E^z Sqrt[Pi] (10178784000 z^(13/2) + 67179974400 z^(15/2) + 134779075200 z^(17/2) + 122344992000 z^(19/2) + 59725512000 z^(21/2) + 17214120000 z^(23/2) + 3090558240 z^(25/2) + 355615920 z^(27/2) + 26447850 z^(29/2) + 1255650 z^(31/2) + 36495 z^(33/2) + 588 z^(35/2) + 4 z^(37/2)) 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]