Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8137)

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`=-5/2

http://functions.wolfram.com/07.22.03.8137.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 23/4}, -z] == ((-2 Sqrt[z] (11916295455736546875 - 9016467891631200000 z - 1016401835056608000 z^2 - 207247208103936000 z^3 - 299835192184012800 z^4 + 166003664014540800 z^5 - 42226634509516800 z^6 + 11819062803824640 z^7 + 4235589373132800 z^8 + 149533581377536 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]]^2 + (35748886367209640625 - 81523897186832100000 z - 316942507705824000 z^2 - 777177030389760000 z^3 - 341160788724940800 z^4 + 182543066018611200 z^5 - 44067021284966400 z^6 + 9410198183608320 z^7 + 4143977720709120 z^8 + 148846386610176 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (-35748886367209640625 + 5259606270118200000 z - 83789398588896000 z^2 - 205652998810828800 z^3 - 340035464518041600 z^4 + 175805412094771200 z^5 - 43781640840806400 z^6 + 10816553012428800 z^7 + 4198635474518016 z^8 + 149258703470592 z^9 + 1099511627776 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(605463150329856000 Sqrt[2] 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]