Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8177)

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`=-3/2

http://functions.wolfram.com/07.22.03.8177.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 15/4}, -z] == ((2 Sqrt[z] (-61665657928875 + 231262818508800 z^2 - 304171042406400 z^3 + 301091497574400 z^4 + 281838102773760 z^5 + 27448196464640 z^6 + 682899800064 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-184996973786625 + 281900150532000 z + 69390806284800 z^2 - 246403913932800 z^3 + 163773127065600 z^4 + 265780073594880 z^5 + 27028598292480 z^6 + 680215445504 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (184996973786625 + 112760060212800 z + 231302687616000 z^2 - 308563059916800 z^3 + 240176893132800 z^4 + 275234905128960 z^5 + 27279149236224 z^6 + 681826058240 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(549038850048000 Sqrt[2] z^(9/4))

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]