Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ck)

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`=11/2

http://functions.wolfram.com/07.22.03.a8ck.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 19/4}, z] == ((2 z (360464994264375 + 385270155270000 z + 223383473913600 z^2 + 370389391257600 z^3 - 81546751180800 z^4 + 4045579223040 z^5 - 62327357440 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (829667666953125 + 645987732390000 z + 356159124921600 z^2 + 325534809600000 z^3 - 79119831859200 z^4 + 4007075512320 z^5 - 62159585280 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (188795486880000 + 572813092726875 z + 492973485404400 z^2 + 290500379769600 z^3 + 351473278464000 z^4 - 80559208857600 z^5 + 4030102241280 z^6 - 62260248576 z^7 + 268435456 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (405424521216000 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]