Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afz2)

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`=-9/2

http://functions.wolfram.com/07.22.03.afz2.01

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), 15/4}, z] == -((11 (2 Sqrt[z] (-3179665125 - 4260438000 z - 1909440000 z^2 - 515973120 z^3 + 52101120 z^4 + 2883584 z^5) BesselI[-(1/4), Sqrt[z]]^ 2 + (9538995375 + 27316926000 z + 14435366400 z^2 + 5295513600 z^3 + 211353600 z^4 - 114819072 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 6 Sqrt[z] (-3179665125 - 2322356400 z - 891072000 z^2 - 173383680 z^3 + 22282240 z^4 + 786432 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(3666124800 Sqrt[2] z^(9/4)))

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]