Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a83d)

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`=-3/2

http://functions.wolfram.com/07.22.03.a83d.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(3/2), 23/4}, -z] == (19 (2 Sqrt[z] (-104476669171875 + 81511702272000 z + 7410154752000 z^2 + 1505555251200 z^3 + 2100156825600 z^4 - 1215509299200 z^5 + 467077693440 z^6 + 171798691840 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-313430007515625 + 722142737316000 z - 12967770816000 z^2 + 4798957363200 z^3 + 2316238848000 z^4 - 1268829388800 z^5 + 366917713920 z^6 + 169114337280 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (313430007515625 - 53492054616000 z + 741015475200 z^2 + 1433172787200 z^3 + 2350301184000 z^4 - 1273076121600 z^5 + 425805742080 z^6 + 170724950016 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(80087718297600 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]