Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afy1)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.afy1.01

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), -(23/4)}, -z] == (1 - (152 z)/69 + (1456 z^2)/1311 - (18304 z^3)/58995 + (2048 z^4)/27531 - (65536 z^5)/2064825 - (243269632 z^6)/3475100475 + (260046848 z^7)/49931706825 - (134217728 z^8)/14230536445125) Cos[2 Sqrt[z]] + (1/14230536445125) (2 Sqrt[z] (14230536445125 - 12374379517500 z + 4365044283600 z^2 - 1067415148800 z^3 + 282291609600 z^4 - 52063764480 z^5 + 222953472000 z^6 - 2634022912 z^7) Sin[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]