Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a88o)

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`=5/2

http://functions.wolfram.com/07.22.03.a88o.01

Input Form

HypergeometricPFQ[{-(15/4)}, {5/2, 23/4}, z] == (19 (2 Sqrt[z] (-37611600901875 - 5094481392000 z - 7410154752000 z^2 + 165987466444800 z^3 + 955760866099200 z^4 - 392966229196800 z^5 + 31612301475840 z^6 - 719407022080 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + (112834802705625 + 187222191156000 z - 75954086208000 z^2 - 373471799500800 z^3 - 755557112217600 z^4 + 374366955110400 z^5 - 31169886289920 z^6 + 716722667520 z^7 - 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (112834802705625 - 53492054616000 z + 74842562995200 z^2 + 297622215475200 z^3 + 868623630336000 z^4 - 385336265932800 z^5 + 31434127441920 z^6 - 718333280256 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(23230443788697600 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]