Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a894)

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.a894.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, -(9/4)}, z] == -((1/(250614000 Sqrt[2] z^(7/4))) ((4 z (76039425 - 107629200 z - 78278400 z^2 - 21319680 z^3 - 6225920 z^4 + 524288 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (228118275 - 91476000 z - 47980800 z^2 - 12165120 z^3 - 2949120 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (684354825 - 144074700 z + 548856000 z^2 + 340300800 z^3 + 90685440 z^4 + 24379392 z^5 - 2097152 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2))

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]