Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae09)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=5, b₁>=-11/2

For fixed z and a₁=1/2, a₂=5, b₁=-9/2

http://functions.wolfram.com/07.25.03.ae09.01

Input Form

HypergeometricPFQ[{1/2, 5}, {-(9/2), 3/2}, -z] == (-1260 + 900 z^2 + 1140 z^3 + 1435 z^4 + 4389 z^5 - 1910 z^6 + 228 z^7 - 8 z^8)/11340 + (1/(22680 Sqrt[z])) ((Sqrt[Pi] (12600 + 12600 z + 6300 z^2 + 2100 z^3 + 525 z^4 + 105 z^5 - 10480 z^6 + 4040 z^7 - 464 z^8 + 16 z^9) Erfi[Sqrt[z]])/E^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]