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

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=5, b₁>=-11/2

For fixed z and a₁=3/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 5}, {-(9/2), -(7/2)}, z] == (1/297675) (297675 + 141750 z + 121500 z^2 + 264600 z^3 + 3175200 z^4 - 125737920 z^5 - 1090627200 z^6 - 1847606400 z^7 - 1225370880 z^8 - 398963520 z^9 - 70495392 z^10 - 7024560 z^11 - 390560 z^12 - 11200 z^13 - 128 z^14) - (1/297675) (8 E^z Sqrt[Pi] (45349200 z^(11/2) + 211048200 z^(13/2) + 290467440 z^(15/2) + 174601260 z^(17/2) + 53892270 z^(19/2) + 9228225 z^(21/2) + 901800 z^(23/2) + 49512 z^(25/2) + 1408 z^(27/2) + 16 z^(29/2)) 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]