Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5342)

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=5, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=5, b₁=9/2

http://functions.wolfram.com/07.25.03.5342.01

Input Form

HypergeometricPFQ[{-(9/2), 5}, {9/2, 6}, -z] == 840/(46189 z^5) + (1/(18162253824 z^5)) ((-330301440 - 330301440 z + 926064405 z^2 - 1422706530 z^3 + 2372361180 z^4 + 9148212168 z^5 + 4623480048 z^6 + 838959264 z^7 + 61821760 z^8 + 1555840 z^9)/E^z) + (1/(36324507648 z^(7/2))) (Sqrt[Pi] (-1091215125 + 2095133040 z - 3491888400 z^2 + 10863652800 z^3 + 22221108000 z^4 + 10027987200 z^5 + 1738184448 z^6 + 125199360 z^7 + 3111680 z^8) 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]