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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{19/4}, {11/2, -(21/4)}, z] == (1/(392071680 z^(9/2))) (-30 Sqrt[z] (12109907484675 + 8161988927400 z + 1676333957760 z^2 + 167458959360 z^3 + 10143006720 z^4 + 417857536 z^5 + 8388608 z^6) Cosh[2 Sqrt[z]] + (181648612270125 + 364627983604500 z + 123798614662800 z^2 + 17112212409600 z^3 + 1302458572800 z^4 + 64945520640 z^5 + 2060451840 z^6 + 16777216 z^7) Sinh[2 Sqrt[z]])

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]