Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bo)

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.a8bo.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(13/4)}, z] == ((4 z (-51234223973625 + 944409658500 z - 606166545600 z^2 + 460660147200 z^3 + 138789273600 z^4 + 15347220480 z^5 + 1027604480 z^6 + 67108864 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-153702671920875 - 26443470438000 z + 242030527200 z^2 + 297805939200 z^3 + 75444019200 z^4 + 8051097600 z^5 + 534773760 z^6 + 33554432 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (461108015762625 + 167160509554500 z + 9821860448400 z^2 - 1469057990400 z^3 + 2017980518400 z^4 + 572604088320 z^5 + 62521344000 z^6 + 4177526784 z^7 + 268435456 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(791844768000 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]