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

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-1/2

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

Input Form

HypergeometricPFQ[{13/4}, {-(1/2), -(21/4)}, z] == -((1/(9398025 Sqrt[2])) (z^(1/4) ((-9398025 - 30431700 z - 22913280 z^2 + 31641600 z^3 - 2097152 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (9398025 + 22913280 z - 16093440 z^2 - 5185536 z^3 + 917504 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (-9398025 + 613440 z + 8957952 z^2 - 737280 z^3 + 65536 z^4) 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]