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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=-1/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {-(1/2), 23/4}, z] == (1/(100663296 Sqrt[2] z^(17/4))) (19 (2 Sqrt[z] (-723647925 - 624864240 z + 11681280 z^2 - 3907584 z^3 + 3080192 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 + (2170943775 + 5182697520 z + 484323840 z^2 + 221184 z^3 - 3735552 z^4 - 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (2170943775 + 551350800 z + 13837824 z^2 - 2727936 z^3 + 3342336 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]