Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8761)

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`=-3/2

http://functions.wolfram.com/07.22.03.8761.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 23/4}, -z] == (19 (Sqrt[Pi] (-872777198928009375 - 372384938209284000 z - 116068032688608000 z^2 - 41615429087232000 z^3 - 29877743960064000 z^4 + 63739187114803200 z^5 - 33994233127895040 z^6 + 34533824129925120 z^7 + 5312896019988480 z^8 + 158741991260160 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-290925732976003125 + 8866308052602000 z - 3439052820403200 z^2 - 3592443023769600 z^3 + 4688589263339520 z^4 - 2416191366758400 z^5 + 2099998422466560 z^6 + 330223929262080 z^7 + 9908489551872 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (872777198928009375 - 558577407313926000 z - 44707686665241600 z^2 - 7765842180096000 z^3 + 7303448523571200 z^4 - 3213544327741440 z^5 + 1881418141532160 z^6 + 323008384204800 z^7 + 9856949944320 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(1595963117949419520 z^(19/4))

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]