Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1733)

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=-11/2, a₂>=-11/2

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

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

http://functions.wolfram.com/07.25.03.1733.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {3/2, 5}, -z] == -((24 (-15 + 19 z))/(20995 z^4)) + (1/(20155200 z^4)) ((-345600 + 92160 z + 264960 z^2 + 161280 z^3 + 13978245 z^4 + 18784890 z^5 + 7561368 z^6 + 1237168 z^7 + 85904 z^8 + 2080 z^9)/E^z) + (1/(40310400 Sqrt[z])) (Sqrt[Pi] (6235515 + 41570100 z + 44089500 z^2 + 16279200 z^3 + 2558160 z^4 + 173888 z^5 + 4160 z^6) 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]