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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {11/2, -(17/4)}, z] == (1/(37509888 Sqrt[2] z^(15/4))) (7 (4 z (-14786211825 - 1689852780 z - 47573568 z^2 + 4603904 z^3 + 262144 z^4) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (44358635475 + 13518822240 z + 669428064 z^2 + 671232 z^3 - 131072 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (133075906425 + 65904258420 z + 8416557072 z^2 + 83568384 z^3 + 18677760 z^4 + 1048576 z^5) 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]