Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8164)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8164.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 3/4}, z] == (1/(1167566400 Sqrt[2])) (z^(1/4) (2 (583783200 + 2674997325 z + 7882926480 z^2 - 14557570560 z^3 + 2608259072 z^4 - 107937792 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (241215975 + 2073511440 z - 13096512000 z^2 + 2542559232 z^3 - 107282432 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 z (2093916825 + 5083238160 z - 13945738752 z^2 + 2581684224 z^3 - 107675648 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]