Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8615)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8615.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 21/4}, -z] == -(((2 Sqrt[z] (1083897269415835875 + 1325557393219659600 z + 113662140694502400 z^2 + 5375869444915200 z^3 - 21630749530521600 z^4 + 3961954542551040 z^5 - 340592047423488 z^6 + 18760417148928 z^7 - 811748818944 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (1806495449026393125 + 3493881308007090000 z - 171950417973734400 z^2 + 37995321485721600 z^3 - 25881150622924800 z^4 + 4297931882496000 z^5 - 358656277217280 z^6 + 19572165967872 z^7 - 871878361088 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (5419486347079179375 - 1079926949747646000 z + 26229724775654400 z^2 + 27991830704947200 z^3 - 25040352205209600 z^4 + 4239970585804800 z^5 - 355668590592000 z^6 + 19436874498048 z^7 - 863288426496 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(33400927184486400 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]