Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a85r)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a85r.01

Input Form

HypergeometricPFQ[{-(15/4)}, {1/2, 13/4}, -z] == (1/(19629342720 z^(9/4))) (Sqrt[Pi] (212837625 + 583783200 z + 7783776000 z^2 + 55351296000 z^3 + 18977587200 z^4 + 1226833920 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-212837625 - 356756400 z + 2595939840 z^2 + 1118085120 z^3 + 75694080 z^4 + 1048576 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (70945875 + 162162000 z + 3265850880 z^2 + 1172152320 z^3 + 76480512 z^4 + 1048576 z^5) 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]