Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a97w)

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=-11/4, b_1`>=-11/2

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a97w.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, -(5/4)}, z] == -((1/(205088000 Sqrt[2] z^(15/4))) ((4 z (4080782475 - 304157700 z + 103118400 z^2 - 101442560 z^3 - 54312960 z^4 - 21233664 z^5 + 2097152 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 - 4 Sqrt[z] (12242347425 + 1419402600 z + 14414400 z^2 - 73328640 z^3 - 32030720 z^4 - 9961472 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (36727042275 + 11253834900 z + 490921200 z^2 - 226195200 z^3 + 477818880 z^4 + 235208704 z^5 + 82837504 z^6 - 8388608 z^7) 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]