Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8563)

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`=-11/2

http://functions.wolfram.com/07.22.03.8563.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 17/4}, -z] == ((-2 Sqrt[z] (83376713031987375 + 110110198797799200 z + 2582524432857600 z^2 - 13490237021184000 z^3 + 2452835008512000 z^4 - 190887147601920 z^5 + 8432463642624 z^6 - 236760072192 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 + 3 (138961188386645625 + 282333843071280000 z + 20400897047731200 z^2 - 15996814073856000 z^3 + 2634172357017600 z^4 - 198643286016000 z^5 + 8645970493440 z^6 - 240518168576 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 2 Sqrt[z] (416883565159936875 - 42350076460692000 z + 16029276251788800 z^2 - 15550570261094400 z^3 + 2605118423040000 z^4 - 197457503846400 z^5 + 8614261555200 z^6 - 239981297664 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (20545965077299200 Sqrt[2] z^(11/4))

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]