Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ph)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a8ph.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, 3/4}, -z] == (1/(9690912 z^(5/2))) (2 Sqrt[z] (-110565 - 168480 z + 3458304 z^2 + 2412816 z^3 + 228864 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + 4 Sqrt[Pi] z^(11/4) (3834675 + 2454192 z + 229632 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (110565 + 21060 z + 1123200 z^2 + 1127016 z^3 + 112896 z^4 + 2048 z^5) 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]