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

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=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(9/2), 9/2}, z] == (1/(4320 z^3)) (-907200 + 529200 z - 204120 z^2 + 61200 z^3 - 15300 z^4 + 3510 z^5 - 945 z^6 + 516 z^7 - 1176 z^8 - 304 z^9 - 16 z^10) + (1/(8640 z^(7/2))) (E^z Sqrt[Pi] (907200 - 1134000 z + 718200 z^2 - 302400 z^3 + 94500 z^4 - 23310 z^5 + 4725 z^6 - 810 z^7 + 120 z^8 - 2640 z^9 - 624 z^10 - 32 z^11) 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]