Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag8q)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.ag8q.01

Input Form

HypergeometricPFQ[{21/4}, {7/2, -(21/4)}, z] == (1/(2215427760 Sqrt[2] z^(7/4))) ((4 z (8871727095 + 5187324240 z + 3011304960 z^2 + 154116096 z^3 - 36503552 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-26615181285 - 18969960240 z - 10785277440 z^2 - 2426609664 z^3 + 173998080 z^4 + 5242880 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (79845543855 + 72118555740 z + 35759465280 z^2 + 14459074560 z^3 + 404324352 z^4 - 150208512 z^5 + 4194304 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]