Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9997)

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=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=4

http://functions.wolfram.com/07.25.03.9997.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {4, 11/2}, -z] == -(30/(11 z^3)) + (51975 + 214320 z - 76740 z^2 + 55680 z^3 + 65552 z^4 + 12032 z^5 + 576 z^6)/(E^z (180224 z^4)) + (1/(360448 z^(9/2))) (Sqrt[Pi] (-51975 + 311850 z + 374220 z^2 - 138600 z^3 + 166320 z^4 + 142560 z^5 + 24640 z^6 + 1152 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]