Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9954)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.9954.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(1/2), 17/4}, z] == ((2 Sqrt[z] (-71641144575 + 127362034800 z + 322429282560 z^2 + 290594304000 z^3 - 1623410933760 z^4 + 450288943104 z^5 - 23706206208 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (119401907625 - 297178081200 z + 185253868800 z^2 + 601044111360 z^3 + 1262652948480 z^4 - 429942374400 z^5 + 23471325184 z^6 - 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (358205722875 - 127362034800 z + 167610643200 z^2 + 548701655040 z^3 + 1308220784640 z^4 - 432773529600 z^5 + 23504879616 z^6 - 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (419647979520 Sqrt[2] z^(11/4))

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]