Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8cn)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8cn.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 21/4}, -z] == (Sqrt[Pi] z^(1/4) (10128266814290625 - 19944894649680000 z + 13789062967680000 z^2 - 6788461768704000 z^3 + 7986425610240000 z^4 + 1622638854144000 z^5 + 74177776189440 z^6 + 1063004405760 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-2437263844178625 + 1449320317830000 z - 639410334393600 z^2 + 419138108928000 z^3 + 97304966922240 z^4 + 4574816501760 z^5 + 66186117120 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + 4 (961375371264000 - 1568127256975125 z + 995694605967600 z^2 - 486152229024000 z^3 + 481877525606400 z^4 + 100572226191360 z^5 + 4623764029440 z^6 + 66387443712 z^7 + 268435456 z^8) Sin[2 Sqrt[z]]))/ (5754397183180800 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]