Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9612)

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=2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=2, b₁=5

http://functions.wolfram.com/07.25.03.9612.01

Input Form

HypergeometricPFQ[{-(5/2), 2}, {5, 11/2}, -z] == (12 (90 + 260 z + 143 z^2))/(143 z^4) + (-417825 - 708960 z - 193956 z^2 + 42624 z^3 + 19600 z^4 + 2048 z^5 + 64 z^6)/(E^z (73216 z^4)) + (1/(146432 z^(9/2))) (Sqrt[Pi] (-135135 - 1351350 z - 1621620 z^2 - 360360 z^3 + 102960 z^4 + 41184 z^5 + 4160 z^6 + 128 z^7) 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]