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

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.afgv.01

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), -(17/4)}, -z] == (1/358205722875) (3 (119401907625 - 263067304500 z + 132897996000 z^2 - 37691438400 z^3 + 9665187840 z^4 - 7153090560 z^5 - 8477736960 z^6 + 180355072 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (358205722875 - 311594283000 z + 110596978800 z^2 - 27881884800 z^3 + 8345272320 z^4 - 14306181120 z^5 + 2979004416 z^6 - 8388608 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]