Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a84g)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a84g.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(1/2), 15/4}, z] == (1/(6900940800 Sqrt[2] z^(9/4))) ((-2 Sqrt[z] (638512875 - 2936044800 z^2 - 6900940800 z^3 + 8838512640 z^4 - 922746880 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 + (1915538625 + 2918916000 z - 518918400 z^2 - 2731622400 z^3 + 8289976320 z^4 - 912261120 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (-1915538625 + 1167566400 z - 2594592000 z^2 - 5020876800 z^3 + 8614379520 z^4 - 918552576 z^5 + 16777216 z^6) 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]