Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7987)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7987.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 17/4}, -z] == (13 (Sqrt[Pi] (3022563043324006875 + 1381743105519546000 z + 570526185504844800 z^2 + 788875713290649600 z^3 - 274391552448921600 z^4 + 33009510069043200 z^5 - 2133948125675520 z^6 + 88683558469632 z^7 - 2667174690816 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((3022563043324006875 - 1842324140692728000 z - 84522397852569600 z^2 + 19902786253701120 z^3 - 2216348880076800 z^4 + 139325111009280 z^5 - 5714856640512 z^6 + 170724950016 z^7 - 4294967296 z^8) Cos[2 Sqrt[z]] + 4 Sqrt[z] (1007521014441335625 + 54061403821286400 z^2 - 17612909780336640 z^3 + 2090930863472640 z^4 - 134490290651136 z^5 + 5575739965440 z^6 - 167503724544 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(11520858757697372160 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]