Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8794)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8794.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 9/4}, z] == ((-2 Sqrt[z] (-92856799035 - 303580236960 z + 1234858141440 z^2 - 633275596800 z^3 + 70407880704 z^4 - 2157969408 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (5065535475 + 172358746560 z + 771770039040 z^2 - 574745149440 z^3 + 68544430080 z^4 - 2143289344 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (15196606425 + 165911185440 z + 823108366080 z^2 - 582543360000 z^3 + 68805918720 z^4 - 2145386496 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (95896120320 Sqrt[2] z^(3/4))

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]