Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afu7)

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`=9/2

http://functions.wolfram.com/07.22.03.afu7.01

Input Form

HypergeometricPFQ[{19/4}, {9/2, -(17/4)}, -z] == (1/(42007680 z^(7/2))) (6 Sqrt[z] (6336947925 - 4633467300 z + 1162909440 z^2 - 175380480 z^3 + 7208960 z^4 + 1835008 z^5) Cos[2 Sqrt[z]] + (-19010843775 + 39248193600 z - 15263186400 z^2 + 2831431680 z^3 - 316293120 z^4 - 17301504 z^5 + 2097152 z^6) 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]