Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7436)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-17/4

http://functions.wolfram.com/07.22.03.7436.01

Input Form

HypergeometricPFQ[{5}, {-(17/4), -(11/4)}, z] == (1/6891885) ((E^(2 Sqrt[z]) (6891885 + 2948400 z + 1555200 z^2 + 2150400 z^3 + 9646656 z^4 + 2391552 z^5 + 8192 z^6) + 8 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-365769 + 731538 Sqrt[z] + 616032 z + 153152 z^(3/2) + 15104 z^2 + 512 z^(5/2)) Erf[Sqrt[2] z^(1/4)] - 8 Sqrt[2 Pi] z^(15/4) (365769 + 731538 Sqrt[z] - 616032 z + 153152 z^(3/2) - 15104 z^2 + 512 z^(5/2)) 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]