Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8493)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8493.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(5/4)}, -z] == ((4 z (2808700557980625 + 628032422902500 z + 242226768168000 z^2 + 424455842764800 z^3 - 467406316339200 z^4 + 496159417958400 z^5 + 190032208199680 z^6 + 12199196098560 z^7 + 221660577792 z^8 + 1073741824 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (8426101673941875 + 279125521290000 z + 284429478564000 z^2 + 301437755942400 z^3 - 284655819571200 z^4 + 197734544179200 z^5 + 91383769989120 z^6 + 6031230894080 z^7 + 110494744576 z^8 + 536870912 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (25278305021825625 - 3977538678382500 z + 443662670682000 z^2 + 714439229011200 z^3 + 2197247612313600 z^4 - 2143572325171200 z^5 + 1812114623692800 z^6 + 748268075089920 z^7 + 48576801538048 z^8 + 885568569344 z^9 + 4294967296 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1078025588640000 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]