Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8qt)

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`=9/2

http://functions.wolfram.com/07.22.03.a8qt.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 3/4}, -z] == (1/(149516928 z^(7/2))) (2 Sqrt[z] (-6081075 - 1916460 z - 3369600 z^2 + 50789376 z^3 + 27509376 z^4 + 2150400 z^5 + 32768 z^6) Cos[2 Sqrt[z]] + 32 Sqrt[Pi] z^(15/4) (6902415 + 3487536 z + 269568 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (6081075 - 6191640 z - 1347840 z^2 + 17971200 z^3 + 12999744 z^4 + 1062912 z^5 + 16384 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]