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

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`=1/2

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

Input Form

HypergeometricPFQ[{15/4}, {1/2, -(19/4)}, z] == -((1/(15207885 z^(1/4))) (Sqrt[2] ((-15207885 + 54428220 z - 68302080 z^2 + 19390464 z^3 + 393216 z^4 + 262144 z^5) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-15207885 + 34151040 z - 288000 z^2 - 7151616 z^3 + 1048576 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-15207885 - 9397440 z + 9661440 z^2 - 638976 z^3 + 65536 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]