Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a7va)

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=4, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.a7va.01

Input Form

HypergeometricPFQ[{-(5/2), 4}, {-(11/2), 1/2}, z] == (2079 + 1260 z - 1260 z^2 + 291 z^3 + 39 z^4 - 40 z^5 - 4 z^6)/2079 + (1/4158) (E^z Sqrt[Pi] (6300 Sqrt[z] + 1260 z^(3/2) - 2331 z^(5/2) + 651 z^(7/2) + 42 z^(9/2) - 84 z^(11/2) - 8 z^(13/2)) 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]