Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an9f)

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=5, a₂>=5

For fixed z and a₁=5, a₂=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=1/2

http://functions.wolfram.com/07.25.03.an9f.01

Input Form

HypergeometricPFQ[{5, 5}, {1/2, 1}, z] == (1/73728) (73728 + 2793375 z + 10409850 z^2 + 11500692 z^3 + 5284056 z^4 + 1160400 z^5 + 126944 z^6 + 6592 z^7 + 128 z^8) + (1/147456) (E^z Sqrt[Pi] (893025 Sqrt[z] + 11113200 z^(3/2) + 29021328 z^(5/2) + 27387072 z^(7/2) + 11616864 z^(9/2) + 2441472 z^(11/2) + 260352 z^(13/2) + 13312 z^(15/2) + 256 z^(17/2)) 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]