Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9fb)

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.a9fb.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(3/2), 21/4}, -z] == (17 (2 Sqrt[z] (-7972289325 - 9859449600 z - 997920000 z^2 - 6488064 z^3 + 217645056 z^4 - 50331648 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 (-13287148875 - 25881055200 z + 864864000 z^2 - 381173760 z^3 + 286457856 z^4 - 65011712 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-39861446625 + 7394587200 z - 222393600 z^2 - 269844480 z^3 + 271908864 z^4 - 62914560 z^5 + 16777216 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (5813305344 Sqrt[2] z^(15/4))

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]