Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9wp)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a9wp.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(1/2), 23/4}, -z] == -((19 (2 Sqrt[z] (5065535475 - 4116752640 z - 254741760 z^2 - 53673984 z^3 - 69664768 z^4 + 50331648 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 + (-15196606425 + 35506991520 z - 1695133440 z^2 + 120766464 z^3 + 72941568 z^4 - 39845888 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-15196606425 + 3087564480 z - 48432384 z^2 - 47480832 z^3 - 75694080 z^4 + 46137344 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2617245696 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]