Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9643)

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`=11/2

http://functions.wolfram.com/07.22.03.9643.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(7/4)}, -z] == (1/(2103464563200 z^(9/2))) (2 Sqrt[z] (-36091940259375 + 8799558768000 z + 565685920800 z^2 - 197188992000 z^3 + 44366192640 z^4 - 16491479040 z^5 + 21485322240 z^6 + 1458569216 z^7 + 16777216 z^8) Cos[2 Sqrt[z]] + 1048576 Sqrt[Pi] z^(29/4) (347985 + 22496 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-36091940259375 + 56922145780500 z + 1665630766800 z^2 + 808474867200 z^3 - 182020608000 z^4 + 49049763840 z^5 - 29711400960 z^6 + 180287963136 z^7 + 11769217024 z^8 + 134217728 z^9) 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]