Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8dx)

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`=-11/2

http://functions.wolfram.com/07.22.03.a8dx.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(11/2), 19/4}, -z] == ((-Sqrt[Pi]) (555179069820375 + 152776549926000 z + 31745776608000 z^2 + 9730506240000 z^3 - 6227523993600 z^4 + 569373622272 z^5 - 19847446528 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (-4 Sqrt[z] (185059689940125 - 33673198759200 z + 974209017600 z^2 - 396443959296 z^3 + 35825319936 z^4 - 1243611136 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (555179069820375 - 439414457882400 z + 19181839622400 z^2 + 427714560000 z^3 - 36810719232 z^4 + 1256194048 z^5 - 16777216 z^6) Sin[2 Sqrt[z]]))/(11544872091648 z^(15/4))

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]