Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9235)

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`=-7/2

http://functions.wolfram.com/07.22.03.9235.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 17/4}, -z] == (13 (Sqrt[Pi] (121120538702625 + 63800119152000 z + 31067884108800 z^2 + 52324857446400 z^3 - 23255492198400 z^4 + 3865848053760 z^5 - 401646551040 z^6 + 40802189312 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-121120538702625 + 65395122130800 z + 4174086470400 z^2 - 1715635998720 z^3 + 265706864640 z^4 - 26502758400 z^5 + 2298478592 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (40373512900875 + 2810243343600 z + 3616901164800 z^2 - 1507236433920 z^3 + 246687006720 z^4 - 25470959616 z^5 + 2499805184 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (808141046415360 z^(13/4))

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]