Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adq8)

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

For fixed z and a₁=11/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.adq8.01

Input Form

HypergeometricPFQ[{11/4}, {-(9/2), -(15/4)}, z] == (1/(68762925 z^(1/4))) (Sqrt[2] ((68762925 - 126320040 z + 25613280 z^2 + 25724160 z^3 + 7418880 z^4 - 11010048 z^5 - 6553600 z^6) BesselI[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (-68762925 + 34636140 z + 38031840 z^2 + 11954880 z^3 + 2042880 z^4 + 7946240 z^5 + 262144 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (68762925 + 57047760 z + 20568240 z^2 + 5214720 z^3 + 2150400 z^4 - 1441792 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]