Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a86j)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.a86j.01

Input Form

HypergeometricPFQ[{-(5/2), 5}, {-(11/2), -(1/2)}, z] == (8316 - 37800 z + 7560 z^2 + 9534 z^3 - 7014 z^4 + 2043 z^5 + 1658 z^6 + 220 z^7 + 8 z^8)/8316 + (1/16632) (E^z Sqrt[Pi] (-83160 z^(3/2) + 29106 z^(5/2) + 12474 z^(7/2) - 13167 z^(9/2) + 5544 z^(11/2) + 3528 z^(13/2) + 448 z^(15/2) + 16 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]