Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9081)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9081.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 7/4}, -z] == (Sqrt[Pi] z^(15/4) (104271021588825 + 526843056448800 z + 183249758764800 z^2 + 16087770316800 z^3 + 479040307200 z^4 + 5152702464 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (1823592771000 + 631547280000 z + 858904300800 z^2 + 3233522073600 z^3 + 31125962178675 z^4 + 11276076586320 z^5 + 1000001318400 z^6 + 29880066048 z^7 + 321847296 z^8 + 1048576 z^9) Cos[2 Sqrt[z]] + (-3647185542000 + 3599819496000 z + 1263094560000 z^2 - 3233522073600 z^3 + 25069861355175 z^4 + 10610914401360 z^5 + 978571077120 z^6 + 29641973760 z^7 + 321060864 z^8 + 1048576 z^9) Sin[2 Sqrt[z]]))/(449906404147200 z^(9/2))

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]