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

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`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(21/4)}, z] == (1/(21590035842375 Sqrt[2])) (z^(1/4) ((21590035842375 + 47105532747000 z + 34400380341600 z^2 + 10607588409600 z^3 + 2285278894080 z^4 + 533787770880 z^5 + 875959418880 z^6 + 537592332288 z^7 + 5502926848 z^8) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-21590035842375 - 29833504073100 z - 12068868520800 z^2 - 2885028269760 z^3 - 598586526720 z^4 - 184772689920 z^5 + 658720161792 z^6 + 40303067136 z^7 + 67108864 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 108 z (799630957125 + 465239829600 z + 131665912560 z^2 + 27605410560 z^3 + 6273146880 z^4 + 3041525760 z^5 + 4616880128 z^6 + 50331648 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]