Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agi0)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.agi0.01

Input Form

HypergeometricPFQ[{23/4}, {-(3/2), -(23/4)}, z] == (1/(299063058525 z^(1/4))) (Sqrt[2] ((299063058525 - 398750744700 z + 83947525200 z^2 - 729144218880 z^3 + 1252841103360 z^4 - 425172271104 z^5 + 152816320512 z^6 + 2399141888 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (299063058525 + 7995002400 z^2 - 700071482880 z^3 + 10481909760 z^4 + 54690840576 z^5 + 14187233280 z^6 + 33554432 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (299063058525 + 398750744700 z + 463710139200 z^2 + 213277317120 z^3 - 127415255040 z^4 + 27991474176 z^5 + 574619648 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]