Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7xz)

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.a7xz.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(11/2), 21/4}, -z] == (221 (Sqrt[Pi] (166986974279750625 + 42158447155440000 z + 7494835049856000 z^2 + 1547320784486400 z^3 + 1146163544064000 z^4 - 212621642956800 z^5 + 12789271756800 z^6 - 354334801920 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((166986974279750625 - 135960992076294000 z + 7762507730208000 z^2 - 87915953664000 z^3 + 14128829890560 z^4 - 821082193920 z^5 + 22397583360 z^6 - 268435456 z^7) Cos[2 Sqrt[z]] + 4 Sqrt[z] (55662324759916875 - 11392818457482000 z + 186559746912000 z^2 + 74519236915200 z^3 - 13448491499520 z^4 + 803591946240 z^5 - 22196256768 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (243827698575605760 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]