Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9663)

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`=11/2

http://functions.wolfram.com/07.22.03.9663.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 13/4}, -z] == (Sqrt[Pi] z^(9/4) (1352359272639375 - 2330219054394000 z + 6579442035936000 z^2 + 2784949009920000 z^3 + 254623909478400 z^4 + 7662663106560 z^5 + 82560679936 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (89190097920000 + 129113284608000 z - 221598716914575 z^2 + 293472363492000 z^3 + 160746400362240 z^4 + 15483504476160 z^5 + 474140835840 z^6 + 5144313856 z^7 + 16777216 z^8) Cos[2 Sqrt[z]] + 4 (11148762240000 + 1274144256000 z + 115862184345600 z^2 - 179830039556475 z^3 + 384039940284000 z^4 + 171259293300480 z^5 + 15826271354880 z^6 + 477955817472 z^7 + 5156896768 z^8 + 16777216 z^9) Sin[2 Sqrt[z]]))/(5743860567244800 z^(9/2))

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]