Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9427)

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`=1/2

http://functions.wolfram.com/07.22.03.9427.01

Input Form

HypergeometricPFQ[{-(19/4)}, {1/2, 17/4}, -z] == (Sqrt[Pi] (6805908734625 + 8799558768000 z + 14079294028800 z^2 + 150179136307200 z^3 + 1001194242048000 z^4 + 366151037091840 z^5 + 29587962593280 z^6 + 693637218304 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-6805908734625 - 1539922784400 z - 6536815084800 z^2 + 46657670492160 z^3 + 21301944975360 z^4 + 1809595760640 z^5 + 43100667904 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (2268636244875 + 1896095401200 z + 3519823507200 z^2 + 58940569497600 z^3 + 22554805862400 z^4 + 1841229201408 z^5 + 43301994496 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (367992797921280 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]