Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9527)

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`=5/2

http://functions.wolfram.com/07.22.03.9527.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 21/4}, -z] == (Sqrt[Pi] (4222757010346875 + 6682164939450000 z + 15839205782400000 z^2 - 118266069841920000 z^3 + 567677135241216000 z^4 + 336401265328128000 z^5 + 39431650148352000 z^6 + 1445927583744000 z^7 + 18360985190400 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-4222757010346875 - 2177890795080000 z - 9855505820160000 z^2 + 22431782880460800 z^3 + 19012623011020800 z^4 + 2383850231562240 z^5 + 89310489477120 z^6 + 1143535042560 z^7 + 4294967296 z^8)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (1407585670115625 + 1583920578240000 z - 9515409415142400 z^2 + 32351906016460800 z^3 + 20597275960934400 z^4 + 2447993450004480 z^5 + 90157067796480 z^6 + 1146756268032 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(545495206330368000 z^(17/4))

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]