Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9595)

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/07.22.03.9595.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(7/4)}, -z] == (1/(127913385600 z^(7/2))) (2 Sqrt[z] (-206239658625 + 7856748900 z - 14789174400 z^2 + 3927813120 z^3 - 1557135360 z^4 + 2087976960 z^5 + 162398208 z^6 + 2097152 z^7) Cos[2 Sqrt[z]] + 131072 Sqrt[Pi] z^(25/4) (272745 + 20064 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-206239658625 + 282842960400 z + 48064816800 z^2 - 15168384000 z^3 + 4513259520 z^4 - 2854748160 z^5 + 17634951168 z^6 + 1311768576 z^7 + 16777216 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]