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

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=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(5/2), 11/2}, -z] == -((21 (-88200 - 45600 z - 16920 z^2 - 5040 z^3 - 1265 z^4 - 288 z^5 - 80 z^6 - 96 z^7 + 16 z^8))/(1280 z^4)) + (1/(2560 z^(9/2))) ((21 Sqrt[Pi] (-88200 - 104400 z - 63000 z^2 - 25920 z^3 - 8145 z^4 - 2070 z^5 - 440 z^6 - 80 z^7 - 208 z^8 + 32 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]