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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=4, b₁>=-11/2

For fixed z and a₁=3/2, a₂=4, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 4}, {-(9/2), -(5/2)}, z] == (1/42525) (42525 + 22680 z + 27000 z^2 + 151200 z^3 - 1587600 z^4 + 18627840 z^5 + 68919552 z^6 + 61516800 z^7 + 22586880 z^8 + 4013568 z^9 + 360768 z^10 + 15616 z^11 + 256 z^12) + (1/42525) (32 E^z Sqrt[Pi] (1193400 z^(11/2) + 2876400 z^(13/2) + 2224620 z^(15/2) + 763488 z^(17/2) + 130827 z^(19/2) + 11514 z^(21/2) + 492 z^(23/2) + 8 z^(25/2)) 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]