Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8f5)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a8f5.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(9/2), 15/4}, -z] == -((11 (Sqrt[Pi] (372020819625 + 175931028000 z + 93829881600 z^2 - 95319244800 z^3 + 13456834560 z^4 - 736100352 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (124006939875 + 1954789200 z - 6136680960 z^2 + 850108416 z^3 - 46202880 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (-372020819625 + 220891179600 z - 6950361600 z^2 + 888053760 z^3 - 46989312 z^4 + 1048576 z^5) Sin[2 Sqrt[z]])))/ (1739461754880 z^(11/4)))

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]