Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8az)

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`=9/2

http://functions.wolfram.com/07.22.03.a8az.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 9/4}, -z] == (1/(70878412800 z^(7/2))) (Sqrt[Pi] z^(9/4) (-11658772125 + 71746290000 z + 45017280000 z^2 + 4899840000 z^3 + 142540800 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 (Sqrt[z] (-498960000 - 824947200 z + 2717408925 z^2 + 2557203840 z^3 + 298129920 z^4 + 8847360 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 4 (-62370000 - 19958400 z - 958003200 z^2 + 4061621025 z^3 + 2759647680 z^4 + 304596480 z^5 + 8896512 z^6 + 65536 z^7) 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]