Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae5z)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ae5z.01

Input Form

HypergeometricPFQ[{13/4}, {-(11/2), 23/4}, -z] == (19 (2 Sqrt[z] (2918248956748125 - 3221258778738000 z + 598634644608000 z^2 - 44763655372800 z^3 + 1563871150080 z^4 - 23026728960 z^5 + 67108864 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (-8754746870244375 + 23004342995634000 z - 7096634633088000 z^2 + 774653799628800 z^3 - 38503376486400 z^4 + 887221125120 z^5 - 6912212992 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (8754746870244375 - 4327549672446000 z + 710516219212800 z^2 - 50047429017600 z^3 + 1681096704000 z^4 - 23907532800 z^5 + 67108864 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (9059696640 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]