Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1267)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=2

http://functions.wolfram.com/07.22.03.1267.01

Input Form

HypergeometricPFQ[{-(7/2)}, {2, 6}, z] == (1/(2170943775 z^4)) (32 (2 z (7144200 - 3274425 z + 2083725 z^2 + 50009400 z^3 - 38188080 z^4 + 4549248 z^5 - 137472 z^6 + 1024 z^7) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (14288400 - 4762800 z + 3274425 z^2 + 13891500 z^3 - 17498880 z^4 + 2223936 z^5 - 68352 z^6 + 512 z^7) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (57153600 - 11907000 z + 10418625 z^2 - 18058950 z^3 - 67863600 z^4 + 72026784 z^5 - 8962560 z^6 + 273920 z^7 - 2048 z^8) BesselI[1, Sqrt[z]]^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]