Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8cf)

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`=11/2

http://functions.wolfram.com/07.22.03.a8cf.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 13/4}, -z] == (1/(5544266956800 z^(9/2))) (Sqrt[Pi] z^(9/4) (1923697400625 - 2841153084000 z + 6685066080000 z^2 + 2263726080000 z^3 + 155226931200 z^4 + 3114270720 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (167650560000 + 204374016000 z - 278486571825 z^2 + 315119019600 z^3 + 133071459840 z^4 + 9523077120 z^5 + 193658880 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] + 4 (20956320000 - 2395008000 z + 164137881600 z^2 - 217138400325 z^3 + 394806258000 z^4 + 139740986880 z^5 + 9665617920 z^6 + 194445312 z^7 + 1048576 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]