Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa20)

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`=7/2

http://functions.wolfram.com/07.22.03.aa20.01

Input Form

HypergeometricPFQ[{-(7/4)}, {7/2, 23/4}, z] == (19 (2 Sqrt[z] (1206079875 - 294053760 z + 5079110400 z^2 + 3882418176 z^3 + 5560139776 z^4 - 813694976 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (3618239625 + 4631346720 z + 9997827840 z^2 + 6185926656 z^3 + 5079760896 z^4 - 803209216 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-3618239625 + 3087564480 z + 7036533504 z^2 + 4985487360 z^3 + 5363269632 z^4 - 809500672 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(108452118528 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]