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

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=2, a₂>=2

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

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

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

Input Form

HypergeometricPFQ[{2, 7/2}, {-(11/2), -(5/2)}, z] == (1/2338875) (2338875 + 1190700 z + 1190700 z^2 + 4989600 z^3 - 32432400 z^4 + 129729600 z^5 - 1029188160 z^6 - 2669276160 z^7 - 1884314880 z^8 - 578135040 z^9 - 88765440 z^10 - 7053312 z^11 - 274432 z^12 - 4096 z^13) - (1/2338875) (2048 E^z Sqrt[Pi] (907200 z^(13/2) + 1663200 z^(15/2) + 1043280 z^(17/2) + 302400 z^(19/2) + 45000 z^(21/2) + 3510 z^(23/2) + 135 z^(25/2) + 2 z^(27/2)) 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]