Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8cb)

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.a8cb.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 9/4}, -z] == (1/(129943756800 z^(9/2))) (Sqrt[Pi] z^(13/4) (-29595344625 + 139272210000 z + 70741440000 z^2 + 6467788800 z^3 + 162201600 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-3929310000 - 1496880000 z - 2554675200 z^2 + 5751709425 z^3 + 4077627840 z^4 + 394974720 z^5 + 10076160 z^6 + 65536 z^7) Cos[2 Sqrt[z]] + 4 (-491163750 + 467775000 z + 104781600 z^2 - 2421619200 z^3 + 8017611525 z^4 + 4349537280 z^5 + 402362880 z^6 + 10125312 z^7 + 65536 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]