Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9611)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9611.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 9/4}, -z] == (Sqrt[Pi] z^(9/4) (-7310050122375 + 53981908596000 z + 42338751840000 z^2 + 6144399360000 z^3 + 268119244800 z^4 + 3944742912 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 (Sqrt[z] (-227525760000 - 448984166400 z + 1873701296775 z^2 + 2340424460880 z^3 + 369190356480 z^4 + 16530186240 z^5 + 245563392 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] - 4 (-28440720000 - 18202060800 z - 594600652800 z^2 + 2999665451475 z^3 + 2580447220560 z^4 + 380981399040 z^5 + 16711655424 z^6 + 246349824 z^7 + 1048576 z^8) Sin[2 Sqrt[z]]))/(56135702937600 z^(7/2))

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]