Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9025)

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/07.22.03.9025.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(1/4)}, -z] == (1/(162225866880 z^(7/2))) (-2 Sqrt[z] (32564156625 + 8683775100 z + 12630945600 z^2 - 23090780160 z^3 + 213818572800 z^4 + 68756284800 z^5 + 4741847040 z^6 + 96239616 z^7 + 524288 z^8) Cos[2 Sqrt[z]] - 32 Sqrt[Pi] z^(19/4) (28143325665 + 8701318080 z + 594961920 z^2 + 12042240 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - (-32564156625 + 34735100400 z + 10525788000 z^2 - 33682521600 z^3 + 87276994560 z^4 + 32743327680 z^5 + 2335656960 z^6 + 47923200 z^7 + 262144 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]