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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(9/2), -(7/2)}, z] == (1/22325625) (22325625 + 29767500 z + 53581500 z^2 + 209563200 z^3 + 4086482400 z^4 - 245188944000 z^5 - 3387900297600 z^6 - 9106454246400 z^7 - 9759627843840 z^8 - 5316929210880 z^9 - 1659591360000 z^10 - 316985598720 z^11 - 38364345600 z^12 - 2978019744 z^13 - 146759808 z^14 - 4409600 z^15 - 73216 z^16 - 512 z^17) - (1/22325625) (16 E^z Sqrt[Pi] (53330659200 z^(11/2) + 371263435200 z^(13/2) + 781499275200 z^(15/2) + 741089034000 z^(17/2) + 376571840400 z^(19/2) + 112627133640 z^(21/2) + 20927710440 z^(23/2) + 2486572515 z^(25/2) + 190580250 z^(27/2) + 9308040 z^(29/2) + 277872 z^(31/2) + 4592 z^(33/2) + 32 z^(35/2)) 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]