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

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=4, a₂>=4

For fixed z and a₁=4, a₂=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(9/2), -(5/2)}, z] == (1/40186125) (40186125 + 78586200 z + 243243000 z^2 + 2918916000 z^3 - 57891834000 z^4 + 1173274502400 z^5 + 8624169066240 z^6 + 15307163827200 z^7 + 11748599251200 z^8 + 4763554375680 z^9 + 1125301708800 z^10 + 162982944768 z^11 + 14784860160 z^12 + 836321280 z^13 + 28439552 z^14 + 528384 z^15 + 4096 z^16) + (1/40186125) (512 E^z Sqrt[Pi] (6014736000 z^(11/2) + 26218080000 z^(13/2) + 38463465600 z^(15/2) + 26793607680 z^(17/2) + 10273223520 z^(19/2) + 2344386240 z^(21/2) + 332012520 z^(23/2) + 29666880 z^(25/2) + 1660707 z^(27/2) + 56058 z^(29/2) + 1036 z^(31/2) + 8 z^(33/2)) 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]