Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7732)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-17/4

http://functions.wolfram.com/07.22.03.7732.01

Input Form

HypergeometricPFQ[{6}, {-(17/4), 1/4}, z] == (1/38188800) ((-8 E^(2 Sqrt[z]) (-4773600 - 26040375 z + 13981860 z^2 - 1249520 z^3 + 1090048 z^4 + 4096 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (52997175 - 105994350 Sqrt[z] + 47589300 z + 46147200 z^(3/2) - 48559440 z^2 - 2097600 z^(5/2) + 14543360 z^3 + 4474880 z^(7/2) + 471040 z^4 + 16384 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(3/4) (-52997175 - 105994350 Sqrt[z] - 47589300 z + 46147200 z^(3/2) + 48559440 z^2 - 2097600 z^(5/2) - 14543360 z^3 + 4474880 z^(7/2) - 471040 z^4 + 16384 z^(9/2)) Erfi[Sqrt[2] z^(1/4)])/ E^(2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]