Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9v8)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a9v8.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(3/2), 19/4}, z] == (1/(37748736 Sqrt[2] z^(13/4))) ((2 Sqrt[z] (337702365 + 257297040 z - 23901696 z^2 + 20963328 z^3 + 7405568 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 - (1013107095 + 2315673360 z + 13837824 z^2 + 27353088 z^3 + 8060928 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (1013107095 + 154378224 z + 13837824 z^2 - 23224320 z^3 - 7667712 z^4 - 1048576 z^5) 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]