Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an1q)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.an1q.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), -(3/2)}, z] == (1/4465125) (4465125 + 17860500 z + 196465500 z^2 - 2724321600 z^3 + 20432412000 z^4 - 277880803200 z^5 - 1485639792000 z^6 - 2140258982400 z^7 - 1403240993280 z^8 - 501276787200 z^9 - 106526044800 z^10 - 14088947040 z^11 - 1180366320 z^12 - 62212608 z^13 - 1985280 z^14 - 34816 z^15 - 256 z^16) - (1/4465125) (8 E^z Sqrt[Pi] (79995988800 z^(11/2) + 273832423200 z^(13/2) + 334855004400 z^(15/2) + 201739507200 z^(17/2) + 68590330200 z^(19/2) + 14131206810 z^(21/2) + 1831293765 z^(23/2) + 151315290 z^(25/2) + 7898520 z^(27/2) + 250320 z^(29/2) + 4368 z^(31/2) + 32 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]