Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8a0)

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`=7/2

http://functions.wolfram.com/07.22.03.a8a0.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 23/4}, z] == (19 (2 Sqrt[z] (104476669171875 - 70049119140000 z + 842905103040000 z^2 + 987361953177600 z^3 + 2610197633433600 z^4 - 753577544908800 z^5 + 46457621053440 z^6 - 856309104640 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 - (313430007515625 + 267460273080000 z + 1871064074880000 z^2 + 1774485057945600 z^3 + 2207954681856000 z^4 - 725929898803200 z^5 + 45929642065920 z^6 - 853624750080 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-313430007515625 + 401190409620000 z + 1344572579750400 z^2 + 1416517582233600 z^3 + 2438454509568000 z^4 - 742289729126400 z^5 + 46245221498880 z^6 - 855235362816 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(58076109471744000 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]