Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a99i)

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=2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.a99i.01

Input Form

HypergeometricPFQ[{-(3/2), 2}, {-(11/2), -(11/2)}, z] == (1/36018675) (36018675 - 3572100 z + 132300 z^2 + 7200 z^3 + 2160 z^4 + 2880 z^5 + 47040 z^6 + 599040 z^7 + 695040 z^8 + 232448 z^9 + 27648 z^10 + 1024 z^11) + (1/36018675) (512 E^z Sqrt[Pi] (360 z^(13/2) + 1680 z^(15/2) + 1560 z^(17/2) + 480 z^(19/2) + 55 z^(21/2) + 2 z^(23/2)) 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]