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

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=-11/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(11/2), 3/2}, z] == (1/3274425) (3274425 - 8930250 z + 13097700 z^2 - 16216200 z^3 + 21621600 z^4 - 40098240 z^5 + 195350400 z^6 + 273490560 z^7 + 122668560 z^8 + 25977840 z^9 + 2908632 z^10 + 175440 z^11 + 5344 z^12 + 64 z^13) + (1/3274425) (4 E^z Sqrt[Pi] z^(13/2) (73256400 + 81192510 z + 33599790 z^2 + 6837705 z^3 + 748440 z^4 + 44520 z^5 + 1344 z^6 + 16 z^7) 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]