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

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=-3/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(3/2), -(3/2)}, z] == (1/81) (81 + 450 z + 18900 z^2 + 577584 z^3 + 1636272 z^4 + 1451736 z^5 + 556608 z^6 + 104719 z^7 + 10002 z^8 + 460 z^9 + 8 z^10) + (1/162) E^z Sqrt[Pi] (216216 z^(5/2) + 2100384 z^(7/2) + 4355208 z^(9/2) + 3376464 z^(11/2) + 1209009 z^(13/2) + 219000 z^(15/2) + 20456 z^(17/2) + 928 z^(19/2) + 16 z^(21/2)) 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]