Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ade3)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.ade3.01

Input Form

HypergeometricPFQ[{9/4}, {-(3/2), -(21/4)}, -z] == -((1/(3132675 Sqrt[2])) (z^(1/4) ((-3132675 + 7160400 z - 6233760 z^2 + 2496000 z^3 + 1417216 z^4 + 131072 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-3132675 + 4654260 z - 2733120 z^2 - 525312 z^3 + 212992 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (3132675 - 2148120 z + 383616 z^2 + 399360 z^3 + 32768 z^4) BesselJ[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]