Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8160)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8160.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), -(1/4)}, z] == (1/(3316950 Sqrt[2])) (z^(1/4) (-2 (-1658475 + 22113000 z + 150872085 z^2 - 417718080 z^3 + 103924224 z^4 - 5521408 z^5 + 65536 z^6) BesselI[-(1/4), Sqrt[z]]^2 + Sqrt[z] (-13267800 + 10356255 z - 361277280 z^2 + 100583424 z^3 - 5480448 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 z (6633900 + 78095745 z - 393773184 z^2 + 102569472 z^3 - 5505024 z^4 + 65536 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]