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

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, a₂>=3

For fixed z and a₁=3, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3, 9/2}, {-(11/2), 11/2}, z] == (1/(1155 z^4)) (-1016064000 + 338688000 z - 101606400 z^2 + 24192000 z^3 - 4702845 z^4 + 769230 z^5 - 108360 z^6 + 13360 z^7 - 1440 z^8 + 112 z^9 + 72 z^10 + 16 z^11) + (1/(1155 z^(9/2))) (4 E^z Sqrt[Pi] (127008000 - 127008000 z + 63504000 z^2 - 21168000 z^3 + 5292000 z^4 - 1058400 z^5 + 176400 z^6 - 25200 z^7 + 3150 z^8 - 350 z^9 + 35 z^10 + 20 z^11 + 4 z^12) 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]