Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afu3)

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.afu3.01

Input Form

HypergeometricPFQ[{19/4}, {9/2, -(21/4)}, -z] == (1/(882161280 z^(7/2))) (-2 Sqrt[z] (-665379532125 + 481608042300 z - 117744580800 z^2 + 16711833600 z^3 - 1000243200 z^4 - 106168320 z^5 + 4194304 z^6) Cos[2 Sqrt[z]] + (-665379532125 + 1368780751800 z - 523309248000 z^2 + 93032755200 z^3 - 10218700800 z^4 - 86507520 z^5 + 67108864 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]