Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9029)

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`=9/2

http://functions.wolfram.com/07.22.03.9029.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 3/4}, -z] == (1/(1622258668800 z^(7/2))) (Sqrt[Pi] z^(15/4) (2673615938175 + 2251466053200 z + 348052723200 z^2 + 15865651200 z^3 + 240844800 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (2 Sqrt[z] (-10854718875 - 6578617500 z - 12630945600 z^2 + 295094016000 z^3 + 274016846250 z^4 + 43146754560 z^5 + 1977615360 z^6 + 30081024 z^7 + 131072 z^8) Cos[2 Sqrt[z]] + (10854718875 - 7894341000 z + 89820057600 z^3 + 123521162625 z^4 + 20877071040 z^5 + 977733120 z^6 + 14991360 z^7 + 65536 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]