Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7w5)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7w5.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 3/4}, -z] == (1/(72100385280 z^(9/2))) (2 Sqrt[z] (-10854718875 - 701719200 z^2 - 1603929600 z^3 + 24519720960 z^4 + 14655641280 z^5 + 1466035200 z^6 + 38944768 z^7 + 262144 z^8) Cos[2 Sqrt[z]] + 16 Sqrt[Pi] z^(19/4) (6700791825 + 3729136320 z + 368309760 z^2 + 9748480 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (10854718875 - 14472958500 z - 3157736400 z^2 - 801964800 z^3 + 8554291200 z^4 + 6835338720 z^5 + 718824960 z^6 + 19374080 z^7 + 131072 z^8) 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]