Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bd)

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`=9/2

http://functions.wolfram.com/07.22.03.a8bd.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 23/4}, -z] == (19 (2 Sqrt[z] (-605964681196875 - 4801548711960000 z + 5683588694784000 z^2 - 3409894449561600 z^3 + 5768502106521600 z^4 + 1283252237107200 z^5 + 64126546083840 z^6 + 993211187200 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-1817894043590625 - 11634521878980000 z + 9657284180544000 z^2 - 5465447853465600 z^3 + 5063298121728000 z^4 + 1244791465574400 z^5 + 63513003294720 z^6 + 990526832640 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1817894043590625 - 7962674415696000 z + 7333830158054400 z^2 - 4451695253913600 z^3 + 5470990221312000 z^4 + 1267600667443200 z^5 + 63879921008640 z^6 + 992137445376 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(120300512477184000 Sqrt[2] z^(17/4))

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]